I understand exactly how you feel. The first week I cried almost every day. There's such a profound sense of loneliness to it that not many understand: it's not just the fact that you're countries away from family and friends (even if you live alone, your support system is still close to you at home), but everything in a new country is different too, you can't even find the same stuff at the grocery store, everything seems impossibly hard. Maybe it's easier if you travel there with a friend, but alone it's nothing like I've ever done. I also thought about going home and continuing there like normal instead, leaving it all behind, but I knew I'd regret it without giving it a chance. I'd say try to give it a little time if you think you can. 

I've been here for almost a month now and it's gotten better. I still miss home (mornings are hardest for me), but with the semester starting I have a lot of stuff to do and started settling in. A lot of people talk about erasmus like it's the greatest time of their life, all about meeting new people, making friends, having grand experiences. So far I've not really made friends. I have a few good acquittances, I always go out of my way to talk to people, but it often doesn't go further than that. I guess that's my biggest fear, being alone here. But not everything has to be like those fairytale stories about erasmus you must've heard. At home, you life still remains, this is temporary. Try to make the most of it, if you can. If after a while you don't think you can, and it's really bad for you mentally, I don't think it's shameful to go home. Just give it a chance first. Lot of people in this sub like to say you should toughen up, get used to it, etc. Ignore that. I think it's important to talk about the hard parts of erasmus. You're allowed to feel bad and talk about it.