Sitting here late at night contemplating that my life sucks right now. No girlfriend, no sex in a quite a while, spend most of my day alone studying, no one to cheer me up at night, I can just hug my pillow. This is not normal, my early twenties should not be spent alone, we need companionship, we were built for it. Ahhh this sucks, whatever, I guess I should just suck it up and hope something comes along one day.
Well if it helps, I can tell you that you're not alone. I'm a graduate student at a medical school, and I've seen countless comments scrawled on the library walls and study desks about being lonely, being horny, people feeling like they're losers, etc.
If you want to enter a relationship, there's nothing stopping you. You won't be able to have a relationship like people new to dating in college did, though - obviously you need to remain diligent about your work and you won't be able to spend 100% of your time with your significant other.
You'll also need to work a bit harder at your relationships. Medical school is a very stressful time, in part because there's very little downtime for yourself. By entering a relationship you will arguably be signing away what little free time you have (along with some time that wasn't free, I'd guess). As you probably know, a successful relationship involves a lot of give-and-take, and at this point you probably don't have much to give. Communication, always key in a relationship, is going to be really critical here. You'll need to work hard at being more tolerant and patient than you might otherwise need to.
Of course, if you end up dating another medical student, then things could be really high-stress for the both of you. Good communication (and good personal compatibility) count for a lot.
It's certainly worth thinking about this now. As difficult as medical school is, things won't become much easier during your residency (certain aspects may become more difficult). While I respect the opinions of those types who want their personal life to
be their work life, I'm of the mind that it's healthy to have both separate, and it sounds like you'd like that as well. Right now you can't separate both, but you can still work on setting up your personal life for a few years down the road when you'll begin to have free time again.
As a disclaimer, all of the above are just my opinions. I'm happily married and my wife is a second-year in medical school, so I have some idea of the stresses of what it's like (but I won't even try to say that I know what it's like - that's one that you can't know until you've experienced it for yourself). Everyone is different, every relationship is different - ultimately we each have to find out what's right for ourselves. Try not to become too frustrated or depressed. Just keep your eyes open, and if an opportunity comes your way, don't be shy about grabbing it.