>Whenever I talk to people I'm constantly telling myself "they don't like you and don't want you talking to them" and basically try to rush through the conversation.
Not sure what to tell you there, cause I'm not an expert. I used to feel the same way about girls but I just ignore that potion of my mind and just go for it anyway. Gotta also work on your self-esteem as well, but you probably already knew that. Maybe Six Pillar of Self Esteem would be a good book for you. I'm reading it atm, it has some insights that weren't obvious.
>So I know I'm capable of it, it just takes me getting over my anxiety to actually let it out.
You are probably stuck in your head. Try meditation to be present to the moment. Meditation has a genuinely healthy impact, it isn't just woowoo spirituality crap. You probably should desensitize yourself to social interactions by having them frequently, so you stop feeling like they are a big deal.
>and I'm not acquainted quite well enough with them to ask for contact info.
You gotta step it up friend, I ask them for their number after the same lecture I met them, lol. You will get used to it, trust me. Just be like "hey we could study together some time".
>but I haven't actually communicated with any of them through that because... I dunno. I feel awkward doing that.
Anything stops being awkward when you do it often enough, that's one thing I learned in the past few years of becoming more extroverted.
Overall, I do relate with you, I had some of the same issues. It's those psychological blockades you need to release.
No, it's all up to you and if you don't put in the effort it's going to remain a problem for the rest of your life. Just being honest.