I'm glad you're thinking about these things, OP. It's really good that you're seeking advice before diving headfirst into medicine.
That said, I hope you won't mind if I play a little devil's advocate here? Not trying to dissuade you from medicine at all. But rather just trying to inject some realism -- at least as I see it, and like everyone else I have my biases, so please take everything I say with a grain of salt, and as you've been doing, continuing asking for other perspectives.
If you want a career in healthcare, there's also physicians assistant, AA, nurse (e.g. NP, CRNA), physiotherapist, occupational therapist, dentist (e.g. oral maxillofacial surgeon, endodontist), etc. These are all likewise respectable jobs that provide plenty of social value. Some of these pay very well and have far better hours than many if not most physicians, not to mention less training involved, less liability, etc. (Lots of physicians have been sued, and EM is regularly exposed to the prospect of law suits more so than many other specialties, though most of these law suits are thrown out, I believe. But it can still be a personally and emotionally stressful and time-consuming ordeal, like having to attend dispositions with lawyers and so on, even if the law suit ends up getting thrown out.)
More broadly speaking, lots of other careers provide social value. Jobs like janitorial work in the hospital or cleaning ORs after operations and so forth are often underappreciated jobs too, yet a lot of good things that happen couldn't happen without their dedicated work and service.
Start-ups are always a bit dicey though. The fact that they're a start-up is why they're always clamoring for money. Not sure if they're the best representative of how life is in the rest of the computer or tech industry, to say nothing of other industries. And I say this as someone very familiar with start-ups as well as the computer industry as I worked for a big famous computer/tech "household name" company that everyone would instantly recognize. The place I worked for was pretty awesome. I sometimes miss it. Anyway, point being, if you can work for a good place that treats you and others especially its customers well while you're doing work you enjoy, where you have a lot of chances to imagine and share your own ideas, to innovate, to create, which has opportunities for you to move into leadership positions, etc., then the work might not be so "meaningless" after all.
That's true of EM, but it's also true of other specialties (e.g. anesthesiology). It's also true of other non-physician jobs like being a CRNA or AA or PA in EM.
EM gets undifferentiated patients. Not sure that fits your "well defined problems" category. In addition, you might never know the patient's specific diagnosis.
The business world is a pretty broad place. It really depends. I'm like you -- sensitive, etc. But maybe surprisingly I found quite a lot sensitivity, compassion, and empathy in the IT/tech industry, just as one example. Especially among fellow geeks. I'm sure there are other examples in other industries (e.g. working for a charity like the Bill & Melinda Gates Foundation).
You can and should be compassionate with patients. Although you also have to be firm with patients sometimes too. Sometimes the best way to be compassionate is to take a tough stance with patients.
At the same time, it's more than possible to suffer compassion fatigue in medicine.
Medicine itself is a hierarchy. Residency can be a brutal rite of passage. You won't necessarily get a lot of compassion as you work your way through med school all the way to becoming an attending. In a sense, medicine is sort of like the military. Obviously it's not the military, but there's a sense in which there's a chain of command, orders are given, need to be followed through, lots of grunt work as you move up towards attending, irregular hours, people barking orders or yelling at you, you're expected to work hard and never complain or at least bite your lips when tempted to complain to attendings or patients, it's difficult to publicly express signs of weakness even though we all are weak in certain ways, there's a certain culture in medicine and in fact subcultures within each specialty which sometimes becomes a bit too much like how the Navy or Army or Air Force might talk badly about one another despite all being on the same team ultimately, etc. Sensitive type of people can be at risk of succumbing to internal breakdowns and the like in the midst of all this.
Also, while emergency physicians are generally compassionate people, I think you could also say they're pretty thick skinned people. You pretty much have to be in order to deal with all the crazy that comes through the ED. If you're too sensitive and empathetic, it might actually be a problem which could impede appropriate patient care.
EM is all about team work. You have to constantly coordinate with lots of different people, from nurses to paramedics to specialists who hate you for calling them up at 3am to come and evaluate or assess a patient, etc.
As a junior doctor you'll have to eventually learn how to lead rather than calling upon others or relying on them. You'll have to be groomed to be in charge of the ED. In this respect you'll be independent and autonomous.
You're also independent and autonomous in that you can work a shift and you're basically done and generally don't need to take the work home with you or be on call. You're not forever ball-and-chained to patients. Although sometimes you can't help but think about things or internalize things especially if you're a sensitive and empathetic type of a person.
However, you're not independent and autonomous in that there's always (mild to severe) pressure from the hospital or others to move the meat. You will have performance reviews (Press Ganey) to see stuff like how much patients liked you and how quickly you discharge patients. You'll always be under observation indirectly or directly by specialists who may second guess you or otherwise challenge your clinical decision and judgments as well as by virtually everyone else in the hospital including hospital admin since the ED is a big "fish bowl."
Medicine can be exciting. Especially specialties like EM, ICU, anesthesiology, surgical specialties, other procedural specialties like interventional cardiology or interventional radiology. For example, med students and even residents often love doing procedures. But once you become an attending, and have done your 1000th procedure, it might not be so exciting anymore. In fact, it might just get in the way of or otherwise impede work flow. Everything becomes "routine" after a while, which is in a way a very good thing since it means you've become expert enough so it has become routine, but at the same time I'm just saying don't think medicine including EM can't become routine.
Not to mention your interests may change as you progress in medicine and life in general. What you like in your 20s may not be what you like in your 40s or 50s. (I'm in my early 30s but already feeling some of this.) It'll take some personal introspection to be able to try and reflect on stuff like who you are, what you like and dislike, where you can realistically see yourself going and doing, etc.
Actually, working in EM requires plenty of multi-tasking. If you want one on one in medicine, it's probably best to do something which mainly involves outpatients. Something like family medicine or general pediatrics (although these specialties have their own pros and cons). They just see one patient at a time. Scheduled appointments too. If someone is very late, you are usually in control of whether to see them or reschedule them. Not like in the ED where anyone and anything can just suddenly show up on the doorstep and EMTALA requires you screen and if necessary stabilize or transfer them.
In the ED, you have to be able to handle the chaos and multi-task really well, take care of multiple patients at the same time, follow-up with radiology, cardiology, neurology, and/or all the other services you might need to follow-up with for not just one but all your patients, at the same time prioritize if a trauma suddenly rolls in, then get back to your patients once it's over, all the while keeping everyone happy including your patients who often think they should've been seen "sooner," etc. EM physicians tend to be the type of people who can learn to manage and indeed thrive in the chaos.
This applies to lots of other jobs outside of medicine as well as lots of other specialties within medicine.
Very true unemployment sucks.
Doctors have great job security compared to lots of other jobs.
At the same time, don't think all doctors will always be able to find jobs. See the pathology market for example.
Even in emergency medicine, while you should always be able to find a job in the foreseeable future, you may not necessarily be able to find your ideal job, especially if you want to end up in a desirable place. Or you may have to settle for less money and/or worse hours or something else in order to have this job. If you're part of a group, then in some locales you could face another bigger group sweeping in and outbidding you and thus losing your contract for a hospital(s). But if you have a family and are settled in an area, and can't move, then you may have to end up working for this new group which you may or may not like. Read
The Rape of Emergency Medicine.
To be fair, this applies to other specialties too (e.g. anesthesiology with AMCs). Plus, EM is a lot more flexible than many other specialties. But I'm just saying don't think job security is necessarily a given, even in medicine. Or at least not without its share of sacrifices.
Again, not trying to dissuade you from medicine, OP. Or from EM. There are a lot of good aspects about EM as well. But I'm just mentioning all this as a sort of reality check, or at least to hopefully give you a better perspective on some of the issues involved. Medicine is a good and even great career for the right person, but it's not perfect by any means, and it's certainly not intrinsically better than or more valuable or superior to many other good careers.