Hmm. I had this problem as well when I was your age and I found that "networking" (I don't know if that's actually the right term or not, but it's the only term I know) really helped out. I found a good friend who had some similar interests as me and after hanging out for a bit he introduced me to more of his friends who all had the same interests. It went on from there. The amazing thing is though, not only did my friendships branch out, but my interests did as well. Because of those guys, I got introduced to cars, boxing, and MMA. Soon enough, I met more people that way. If you can find someone of like interests, it doesn't take much to expand from there. If I could give some advice though? Try to keep your circle of good friends small, maybe five or six max. Otherwise you'll soon find you have as much stress maintaining your new friendships as you did being alone.
Yeah, I should just keep trying to put myself out there and sooner or later I'll find at least one person whom I feel I can connect with, and it can keep building from there. It can be tiresome to try and try and never feel like you're getting something from the effort you put in, but I'm thinking it's better than not trying at all...! A circle of 5 or 6 friends is something I'd absolutely love to have. I agree it would be tiresome to try to maintain many more friendships than that!
I'll be entirely honest here. It might work, sure - but finding that first person is a feat in and of itself. Hell - if I had found that person, I might not even be here.