What kind of doctors have told you you're fine?
Because it sounds like depression to me.
I wish I could help you more, but in my personal experience there is no real quick fix. And, side note, I guess, I just want to say that 'all the things other people do' doesn't make them normal either. I feel like there is no such things. Everyone enjoys different things, so you don't have to feel for not enjoying the same things as them. Some people like to go see movies, others like to go hiking, some like to play sports, other like to paint, draw and write. Some like to go on walks - explore their town, some people enjoy trying new foods and being adventurous that way. Some people like to cosplay, do math, make things out of paper, travel. There's an endless list of things that people like to do and I think you're hurting yourself by telling yourself that you don't fit into a category, when in truth, you don't have to fit in anywhere.
I mean there are certain things I do with some friends, but not others, because I know where their interests lie. Lay? Guh, I hate that word.
And I don't mean to prattle on about it, I just...feel like I can relate. I deal with my own depression on a daily basis. And the only thing that helped me was medication, therapy and time. (which I know you guys joke about all of the time, but therapy straight up saved my life, so it's near and dear to my heart) What I liked about therapy was it gave me the tools to deal with my life, my sadness, the stress I felt in a healthy way. So, now that I have the tools, I don't have to take medication or go to therapy.
Anyway, I talk to much. I'm sure other people will have better advice. I just want you to know that you're not completely alone and I hope you can find something you enjoy doing. And I mean going out and doing. Don't just sit at home watching anime. Go out, explore, find something that interests you.