Perplexed,
Please do not be offended. I think you will be okay if you chill and not worry too much about women right now.
Y'know what, it might be a lot better if you deal with the Avoidant PD first, then worry about a girlfriend. APD is complicated and can take some time to treat. It's really important.
As far as working out and such: either do it alone, or with someone equally weak/weaker/less athletic than yourself. Not joking. It'll make you feel good, and give you plans for after school.
Pack your schedule with places to go, or activities to do. You'll end up meeting people who like you, simply by sheer amount of people you encounter and by being involved in your own interests.
Soz made a good point: Talk to shy girls and the like. No intentions: just practise getting over "what they think matters/reflects who I am" by saying "Hello" whatever and leaving it at that. Whatever. Give things a shot. Step back from the situation and ask yourself "Did anything explode? Did anyone throw rotten tomatos at me?" . No? Well, then, good. lol.
Chai, that's exactly the sort of situation where I meet most of the people that end up meaning something to me: Just happen to be somewhere, and chat someone up, or go with the moment.
Little moments like that are the best!
Peace out.