Being 6'2" and 165 pounds is on the thin side. 6'2" and 230 pounds, especially if you have a lot of muscle mass, seems healthier to me. And regardless of whether you think you are overweight, I would much rather be with someone who has a little "extra meat" than someone who is skinny. Personally, I would also rather be with someone who does have flaws with their body. Women are far more self-conscious about their bodies than most men are, so if the guy we are with also has some imperfections, it makes us feel more secure. I'm 30 years old and when I was 25 I thought I was so fat. I look back at pictures now and realize I had a great body and that my thinking was incredibly skewed. We are always our own worst critics. If this girl is following you around at the gym and staring at you, she obviously likes what she sees, so I think you have absolutely no reason to feel insecure. And if a girl doesn't want to be with you because of your body, chances are she's not a girl you want to be with for the duration anyway, as she's going to be high maintenance in other areas of life and a girl like that will never be satisfied, no matter who she is with.
Good for you! Quitting the drugs is so huge and something you should be very proud of.
Yes, muscle weighs more than fat. You've been working out so that's why you're gaining weight.
None of us can give you a definite diagnosis, only a Dr can do that. We're here to listen and help if we can though.