hello friend i have read your story,
I'm going to have to be honest and tell you that when you and your friends teamed up against the girl, you messed up with her. From what i read, the girl was in a bad place mentally, and was in need of professional help. Her 'crushes' seemed more like a sort of cry for attention, or what happens when someone feels too alone and unwanted without getting help. I'm not sure if you were her last friend, but if you are, that means she is completely alone now. Getting teamed up on and yelled at, especially by what you'd consider your last friend is very rough. But you shouldn't be blamed, from what I have read, part of it was peer pressure as your friends were the deciders in standing up against her, and I'm sure you got lost in the moment, especially because you are also in a bad place.
I feel like you should apologize to her in some way, I'm sure both of you have a form of depression, and that's a serious mental disease that is very deadly to fight through alone.
I'm going to disregard this girl now.
You feel alone and you're bored when you're at home. I have been through this too. I'm sure you miss NYC and that is completely understandable. I am not sure if you have the option to return, and I'm going to assume you don't.
Your profile states you're 14, so I'll assume that this is your actual age. I was going to suggest looking for volunteer jobs, because it fills some of your time, you get to write it on your CV, and you will meet interesting new people. But since you can't I will suggest you to find a local group or club that you have interests in, or are maybe curious about. There's a lot to do in life, personally I recently picked up skateboarding, which is something I had never thought of doing before, and I am in love with it. It's a hobby, something to fill your time with, and you will meet new people as well. Try looking for something like this, maybe a sport or a creative outlet, that allowed you to fill your time with something you enjoy and can meet people with.
It seems to me that you're not always enjoying your time at your computer, and this can be because you are having a depressive episode, or because you are actually bored and want to find something new to do.
Because of my experience with depression and my suspicion that you might suffer from it, I also advice you to look up help, or inform your parents. The latter is very scary and a big step, but I am sure that your parents would understand. Depression is common for young adults that moved away from their home, especially when it's a whole new continent.
The UK and the US are also very different in culture, so you might also be suffering from culture shock, without even being aware of it.
I don't know what to tell you about school. School sucks, my remedy is to always wear ear-buds and to play my music whenever I am not with my friends. I enjoy surrendering back into my little 'zone' i guess. If you are capable of doing this I suggest getting Spotify premium if you can afford it and have 3/4G. If not, you should look for an older iPod, they're cheap these days which means you don't have to worry about it if it gets stolen.
Also, cliques are everywhere in life, but in highschool they are the worst. In college, that is if you will go, you will surely find a clique to match with, you sound grown up for your age.
I don't really know what else to tell you, it's good that you didn't watch Tokyo Ghoul I guess because the anime is very bad, haha!
I hope you can clear up your mind and I hope my post helped, stay safe I'm rooting for you!!
By the way I might be in London soon to visit a friend, if you would like to hang out at all, let me know!
