Kiwong is right: Based on what you've revealed, you are no sociopath. I'm so sorry you're in this rut. I'm not sure how old you are, but I have found that the older I get, the more difficult it is to form relationships with people--and I honestly don't think this has much to do with any of our social phobias. Sure, this may make us all the more anxious, but . . . there's just this implication that, for the most part, when you're an adult, things have been stabilized and while meeting new people might happen, those with connections are content with what they have. My husband and I have been amazed just by the lack of neighborliness on our block; people seem content with who they know--and not interested in forging new relationships. It's very disconcerting, I know.
I'm wondering if signing up for some class where the focus is on doing things with your classmates might help. Like, conversational Spanish, perhaps. Or, a group that goes on hikes. I know someone else mentioned hobbies. I just feel like there are situations where people may be and they may not be open to striking up a conversation--even if you felt comfortable doing so; honestly, a coffee shop may be such a place (at least from what I've observed). If you like animals, maybe you could volunteer to walk dogs at a shelter and meet others that way.
What helped for me is volunteering at a crisis center's food bank. I don't know what the deal is, but people who volunteer there, for the most part, are pretty awesome. Maybe they've all hit rough patches, themselves, and just know the importance of being nice. I REALLY hope you can find a place like this. Obviously, it would be awesome if some serendipitous event led to a friendship, outside of any hopes/plans for such a thing. I just have found that this doesn't seem to happen as much as it used to for me.
Feel free to contact me, too. Maybe you could paint scenarios you've been in where you wanted to talk to someone but it didn't pan out for whatever reason, and some of us here could help "troubleshoot".
Best to you!