Why do I feel like a mentally ill person?

I think the two are intertwined. Self-confidence is a very necessary trait to not only have, but exude to attract girls (as opposed to being y, mind you). That being said, I think that if you were more confident your depression would fade and your luck with girls would improve. Confidence comes from knowing yourself, who you are, what your limits are, and what you have to offer, to people, a gf, etc.