forget the meds, they're not for everyone. I feel, in western society, we're too focused on 'quick fixes', what pill can I take to sort this or that...
Have you considered counselling or group therapy to work through what's going on in your head?
Main focus should be working on your depression, after that the confidence in yourself will grow and the anxiety will start to drop making it easier to meet people.
I know what you're saying about the gym, I joined one years ago as a way to meet people, I ended up just doing my own thing and not really talking to anyone, even the classes didn't help.
Have you thought about other fitness activities? indoor climbing, running club something along those lines?