Well, as it stands right now, if you are not a US citizen, you CANNOT be accepted into the Nuclear program. That would be as either enlisted or officer.
As far as going to college or joining the Navy, well, that is a personal choice.
Keep this in mind, if you go to college and for some reason don't like it or want something different in life, you can always leave and pursue something else. Once you sign that contract, you are OBLIGATED to complete it. Sure, things can change (medical, hardship, poor behavior, etc.), but for the most part you are locked into the Navy for a minimum of six (6) years (enlisted) or five (5) years for officer (that five is what i recall. I have been retired since December and not done research on Officer programs for some time. So, take that with a grain of salt.).
Work on that citizenship issue and best of luck!