As an EMT, you're a first responder and you get a lot of good patient contact but you really don't get to see a lot of the physician side of medicine. You'll want to get into a doctor's office and/or OR and see what a doctor's daily life is like and how they make their decisions/how they interact with patients.
To do this, you can shadow a physician. Talk to the doc, see if you can follow them around and just get a feel for what it's like. You'll want to do this for an extended period and log a lot of hours (possibly in a few different specialties). This is really the best clinical experience you can have in terms of getting a feel for medicine and showing a medical school that you know what you're in for. Just as an aside, after an extended period of shadowing, you can ask these doctors for a letter of recommendation which will also help your application.