It is difficult (but not impossible) to get into medical school as an engineering major, so that has to be your first decision. This is particularly true at Berkeley, where you will be competing for grades with other students who are as academically gifted as I assume that you are. The road would probably be easier for you in a less rigorous major. The NROTC scholarship can (and probably will) restrict your flexibility to change your major, even from nuclear to bioengineering. As the financial benefit of the scholarship is not an issue, you may be better off without it.
On the other hand, Berkeley has a common first year engineering curriculum, so you don't have to choose between nuclear and bioengineering until you are a sophomore. If there is a part of you that is saying "maybe, like many other students who declare pre-med, I might change my plans during freshman year", you might want to give NROTC a shot. You incur no obligation for the first year, and next Spring you will be in a better position to assess your future interests.
In any event, if you are committed to medical school and engineering, you should meet with a pre-med advisor at Berkeley right away to get a realistic assessment of your situation.