Good on you, it sounds like you really are making great, healthy choices for yourself, you should be very proud of yourself. Being that you can talk to women in general is a really good sign, that is already a big step in the right direction.
I'm not into the whole hook up culture either, it was never for me.
Having a real connection with someone is kind of rare so don't be thrown off by rejections, it's almost lifes way of weeding out the people who aren't right for you. If you have a real connection with someone, they're not going to scare off so easily unless they're carrying baggage from past relationships, etc.
I wouldn't even really try too hard at flirting if it doesn't feel comfortable and natural to you plus you don't want to come off as sleazy. Slow it down and try to just get to know girls you're attracted to without freaking out about having to make a move. Focus on trying to develop a friendship with a girl you're attracted to first, that way you can learn to become comfortable around someone you have a spark with, then when you feel safe to move forward then you can at your own pace.
It's lucky you didn't end up with the girl that thinks mental health issues aren't real. Just a tip, just because you're attracted to someone, doesn't mean they are a healthy person for you. Make sure you consciously choose someone who is right for you.
Also remember that there are a lot of women out there who are just as anxious talking to men as you are to them. What are the types of women you are going for? I ask because I have heard a lot of nice guys complain about women wanting bad boys when they themselves are chasing the wild, confident, party girls and not getting anywhere so it's pretty much the same thing haha.
You need to stop believing that this is something that is impossible, your brain has a way of making your beliefs a reality. If you believe it's impossible, your brain will block you so to speak and make you feel more anxious during interactions, it becomes self fulfilling.
I think you will be fine, if you just take the pressure off yourself, believe that it is possible for you, keep working on yourself, it will happen in time.