You can go to medical school after completing NROTC.
What will happen is when service assignment comes around during the beginning of your senior year, you submit a package to a Navy board to be selected to go to medical school. They usually will say yes. At the same time you apply to both civilian medical school and the military medical school.
After graduation, instead of going out into the fleet, you go to med school. You are active duty and get paid, but your main focus will be going to medical school. Once you graduate from medical school, you will obviously have an additional service commitment, though I don't know what it is. I'm sure you could google and find out.
We have a couple from my unit who are going to med school after graduation. It's a pretty good deal... free college AND free medical school.