The two problems are interlinked, but can certainly be dealt with seperately (although in much the same way).

How long have you been into PUA stuff?

Okay, my stance on your situation:

This is easy to say, but it's your life - you make the rules. Only you can decide whether to allow yourself the freedom to change and let yourself be happy.

Seriously, scare yourself. The first sentence of the Venuasian arts handbook is something along the lines of "Nature will unapologetically weed your genes out of existence if you don't take action and learn how to attract women now." Carries a bit of a kick, right?

Right now, I would say ignore the approach anxiety. Do not worry about approaching girls just yet, but at the same time, do not use the next step as an excuse to put this off eternally.

1) delete any "feel-bad" music you have. Replace with something feel-good and higher energy. Music is like a global energy source and you can usually refuel yourself with this.
2) look into neuro-linguistic programming - you don't need to go in depth here, but understand the basic concepts and how it can help you.
3) write yourself some affirmations and repeat these to yourself constantly. Take a look around for something that fits you or write something of your own - ultimately you are telling yourself that you are strong, powerful and have the ability to take what you want in life. A girl deserves the chance to make a choice about you, and you are strong enough to allow her that choice, rather than walking by.
4) Work on the eye contact as this will be vital in the future - begin with the mirror, and make eye contact with yourself. Next use a friend or family member, or even your psychiatrist. Build yourself up through desensitisation until you are able to make eye contact with people in real life.