Give it a Try!
I always thought that I would not be an exchange student you feel homesick. However, it can be happened anyone and everyone. So, if you feel homesick or at least there are some symptoms, the first best thing would be accept this feeling. It doesn't mean that you are a failure. It means that you love you family and loved ones more than you think and you are doing something you have never done in your life before such as living in another country on your own and the country no one speaks your language. That is perfect! I think the only thing that you need to do is to change your perspective to the situation.
Moreover, you can do so many great things to go over your problem. You can write your journal, or you can record yourself and explain what you exactly feel. They are perfect memories when you are back home and you wanna remember the days in exchange. You may say who wanna remember bad days but you will not remember them as bad days. You remember them even though you feel frustrated sometime, you did your best to get the most of the exchange experience. The second thing you can do is to meet people. I heard that so many friend of mine told me people in the class do not care about others and go out after they are done with classes but it is not true all the time! You can be active in the class and maybe people who are suffering want to get help from you to be successful in the class. That is for real. It happened to me why don't you? Additionally, many of my friends also told me that people who go to exchange do not have chance to meet with locals. I do not believe that! If you wanna be friends with people they will not reject you. That is of course, if you wanna be friends with locals. Meeting with one of the locals is enough because they have so many friends and the circle is getting bigger if you give it a try. I did not talk about meeting to exchange students because it is generally easy, The only thing you need to do is go to EVENTS. It is the best way to make friends. For example, in each time I do not wanna go to events, I forced myself to go and I am so happy that I did and doing!

Sometimes life puts you in very difficult situation but you need to remind yourself that everything will be fine at the end. Go out, see sunset or sun rise in different parts of the country. Go to classes with you PJ's. Speak with the first stranger you see. Go to the comic show. Go and buy the kind of a book you have never read or go and watch a movie. Found the best coffee shop in the town. Taste each and every single special food in the town. Cook something you have never cooked before.
There are so many things that you have never done and may like it.