There are millions of people in our country who live alone and end up spending a lot of time alone. They aren’t losers because they are alone. That is the first belief that you have to work on changing. There is a difference between being alone and being lonely. Many people are quite happy being alone and doing things on their own.
You sound like you’re depressed. In answer to every suggestion, you reply with some version of how it wouldn’t work. This is called hopelessness. Go to the counseling center to talk to someone. Unless you think it wouldn’t work.
Think about this: at your current school, you’re not the only one going through this situation of having no friends. I don’t think it’s a good reason to switch schools…
I’m almost in the exact same situation as you, except I go to a relatively small school without Greek Life. Friendless sophomore male (except I’m not athletic and I never really had close friends, if any friends at all. Plus, I’m guilty of sitting by myself in the dining hall almost all the time). Personally, if I found that there was nothing but Greek Life, I would’ve transferred almost immediately. I have to warn you that although a lot of it is Hollywood/urban legend, I would ask if you want to risk hazing. I’ve seen quite a few horrific real-life examples in the media. Anyway, have you tried counseling services or gone to any clubs or other student organizations? Do you have a job? It might sound a bit hypocritical on my end since I haven’t found much success in them, but I have faith in others if I can’t have faith in myself.