I figured I'd chime in on this having gone through the waiver experience myself. Here's the deal-- I'm not a recruiter, so this is just my two cents; I've gone through it but I'm no expert. Your first step will be MEPS/DoDMERB. You will be given a monster form you have to fill out of YES and NO boxes. This is a little mantra that goes, NO- Numerous Opportunities, YES- Your enlistments stops. Read the form carefully and don't volunteer information they don't ask for. DOD is having you fill that out as a CYA on their part. Read the questions carefully--- you may find your box that you thought you would have to check isn't there! I was concerned about a High School ADHD diagnosis and medication, but guess what? Navy doesn't know because they never asked. Now I am not saying lie. That's a bad way to start your career BUT it sounds like you dont have an issue so dont give the bureaucracy a reason to think you do. There is this rumor that goes around that DoD does a big check on everyones insurance history. I am quite certain that that is a myth, but feel free to correct me. Can you imagine how expensive that would be?
Now, Medical is actually only PART one. Since all officers (and I think staff) are required SECRET clearances, you may have to fess up when it comes time to filling that out. If THEY ask . If they do, for the love of God don't be less than truthful. That is a real investigation and with all these traitors coming out and leaking intel, the pressure is on for these investigation teams. They however, are a bit more case by case. If it is an issue you will have a chance to talk it out with your investigator and as long as you don't have any other issues, you should be good to go. Again, you may want to be prepared with documentation and some character witnesses if you have a murky past.
Finally, worst case scenario-- you have to check the box YES. Provide as much documentation as possible. See if that therapist could write you off as a misdiagnosis or something. In my experience, most non-government health care providers are very supportive of people trying to serve. Submit that and hope they don't hit you on it. If they do, still not the end of the world. Go see if you can find an Army doctor to recommend you for a waiver.
Lastly, understand in the unlikely event you are disqualified that there are other ways over serving. In many ways there are BETTER ways of serving.
I hope that gives you some confidence, good luck.