Good to hear. Don't let anyone put you down about starting early. You're starting early, but you're doing so because you are very concerned about reaching your goal. Nothing wrong with that.
During college, major in something you like. If you're dead set about medicine and know you'll go to med school for sure, then major in something you like rather than something you can find "jobs" with. If you have ANY interest in something like Philosophy/Art History/Literature, then major in them.
A lot of people would say you cant find a good job with that major--maybe so, but if you're committed to medicine, then this won't be a matter for you.
As a foreign country student, your goal is to become very proficient in English (unless you already are). Majoring in those things will let you do that. Of course I'm assuming sciences aren't your weak-point. In that case, sciences will come easily for you, so concentrate on your reading. Read editorials of any newspaper everyday you can. I wish I did that...
Maybe your idea of fun is to read... or watch TV... or run/exercise... or drink and go to parties. Whatever it is, do some of that. Don't feel obligated to do it--do it when you need to do it. Everyone's different. You don't have to enjoy poetry or being drunk...
If you do nothing else, take your pre-med requirements in the first two years (hopefully) and ace them and shadow doctors. Go to Columbia Presbyterian and look for Residents to shadow--just ask three, I am sure you'll find one who says ok.
Don't worry about what major you want to choose--for the first two years, just try to finish the premed science, math and humanities courses. Then the second year, you can try to specialize. Whatever your major--it doesn't really matter.
Ace whatever classes you take, and try to get rid of the pre-med requirements first. Shadow doctors first off to confirm your decision to yourself. Do research if you can (but first shadow someone).
Good luck, and do yourself a BIG favor and read a whole lot. And whatever your idea of fun--do it. It really helps.