Tough to say; my experience is with the Army, and that was twenty years ago.
I don't know if enlistment waivers are still authorized or not; I would recommend a complete physical by your family doc, for starters, and speak to your recruiter about your concerns. Just remember that until you sign the papers, the recruiter will, in some ways, "work for you" if you're a good prospect. Use that to your advantage.
How's your weight, physical fitness levels? Those are of importance as well. Grades in school OK? The trick to getting in right now is to make yourself as attractive as possible to the service - good grades, no disciplinary/legal problems, good physical fitness, the ability to learn.
Good luck!
