Medical History and Military

So I'm filling out my application or whatever for the Coast Guard and I've seen some questions about seeing a therapist and prescribed medication. I checked no for them since I haven't been on prescription medication in like a year and that was only for like a month (antidepressants) and haven't seen a therapist in like a year either. How much does the military actually check into your medical history? I've changed health insurance companies since then so if I just don't list my previous health insurance would they be able to see any of that info? Would I get disqualified for any of this? I'm in great mental health now and more than capable to serve. How much do they actually check into this kind of stuff?