Should I Leave Study Abroad Early?

I'm a US exhange student studying in the UK for the fall term, and this experience has been less, WAY less, than easy. I knew this wouldn't be easy, but I didn't know it would be this hard. I've struggled so much with my mental health since I got here, but most of all over the last three weeks. I've cried every day for the past two weeks and can't get work done, no matter how long I sit at my computer or read. It's like I'm just stuck and I don't know what to do anymore. I have the option of going home early and finishing my final assessments online, and I was very close to deciding to do that, but I have some things I still want to do in the UK and people I don't want to leave behind...Everyone at home, too, keeps saying how brave I am and how jealous they are of me for being able to study abroad. I don't want to let these people down or make it seem like their support was for nothing. I know I can't go on any longer the way I am, but I don't know how to change how I feel without changing my environment to somewhere where I am more comfortable. Then again, I don't know if I would feel any better going home, or if I would maybe even feel worse because I left early or "gave up". I want to save my mental health as much as possible, but I don't know whether staying or leaving would be the better option for that at this point. What should I do?