Depression clouds our thinking sometimes. Perhaps once you begin taking one, you will be able to answer many of those questions. I'm not sure my posting on all you addressed would do you as much good now, as it might in the future?
But I'll try
Having a mental disorder doesn't mean crazy nor "nuts." It means something is DIS ordered... something in the brain chemicals is not in order and needs assistance to regain it's balance.
I prefer the term mentally unwell. It isn't a purely psychiatric problem; depression is a medical illness. Why on earth would they have all these drugs for a purely philosophical disorder???? If you were physically healthy and took meds for a problem you didn't have, (aside from the side effects

) it wouldn't do a thing "for" you. The very fact that medicine helps shows that it's a medical problem. The medical problem just happens to affect the way we think about how we feel.
There is no basis for feeling hypocritical regarding your course of study. There's no connection whatsoever. I think you might find your inside T by reviewing the 10 common cognitive distortions (it's pinned to the top of the psychotherapy forum.) TC!