I think you're being overly negative. You're in a wonderful situation where you can both learn to be independent and go home practically every weekend. Talk to some of the nice people you met about your homesickness, try to distract yourself.
The reason why you're homesick is that you miss the people you love. However, you're not going to love them less when you're somewhere else for some time. They're always with you in your heart and you can call or do whatever. I think you should stick through it.