Yup. Like Mike suggests, one step at a time. Any reputable flight company won't even look at a resume with less than 3 years of experience. Even then, they'll take the guy with 4 years over the guy with 3 years, and so on. You wouldn't want to work for one that's less than reputable...it's a good way to end up dead.
When you're done medic school, you can start looking at additional training. Advanced pharmacology, Advanced Trauma Life Support (not ITLS - Advanced), aviation related training. I'm not sure what the States have, but in Canada we have a training program put on by the Canadian Aerospace Medicine and Aeromedical Transport Association which is pretty much compulsory. You could even become a pilot, it won't make much difference for employability options, but it makes you more attractive as a candidate because you'll understand the aviation aspect much better.