Three weeks does not a relationship make... You are still in the "sex haze" part of the relationship...
However.... if either party goes into a relationship worrying about being hurt, the relationship is pretty much doomed from the start, because they are not going to invest their all in the relationship, they will hold back.
Medical school, from all I have heard, is a tough few years, as is the residency that follows. That's a lot of work and a lot of pressure on someone, plus to add in a long distance relationship... doesn't sound like anything would get her full attention. Plus you doing all the travelling for the relationship will eventually lead to some resentment on your part that y ou are doing all the work.
I'd split apart now, and it it's meant to be, that when you are both finished with school, see where each other are... Don't give up the friendship, just the romantic part of the friendship.