Assalamu Aliakum/Greetings friends,
During the past 5 to 6 years, I have been becoming more and more homesick, I really badly want to go back to Pakistan and go on with studies over there. (It is not because I have no friends, please do not get me wrong. I have plenty of great friends, Irish, Italian, Greek, and lots of Armenian and Brazillian friends, you name them. I have a great social life as well ). But I don't belong here, there is a saying in pashto; zama ki aw pada ki da zmaki aw da asmaaan parakh de (meaning between me and him, there is land and sky differences) What I'm saying is, there is land and sky difference between me and Americans, I don't share the same language (although yes I can speak English) culture, religion etc...
I know exactly how you feel, as I feel the same way. I can't wait till I get out, too and I'm a lot older than you are. And I'm asimilated in this culutre quiet well, too but it's not me. And every time I visit Pakistan, I get this sense of belonging that I dont get here.
For your case, since your parents are here with you, it'll be hard to break away from them and start a life in Pak. Then you'll start to miss them there and they you here.
Seems like your're around 20. I would say start telling your parents how you feel and see where they stand on this. Meanwhile continue your education here. Keep evaluating yourself, to see if you still want to move back.
And if in the next two to three years or whatever, you still want to move back after your education, I would say go ahead with it. Becuse if you wait too long and get a job here and settle down, it'll be a lot harder to move back. Like it has for me, with kids. But I'm still adamant about moving back.
Whatever you decide, best of luck.