Hang in there it will get better! Honestly!
I dont remember being homesick as it was a LOOONG time ago that I went to Uni, but both of my girls were horribly homesick (they have both just graduated after 5 years (medicine ) and 3 years (nursing)
DD1 I had to skype every evening for the first two terms. She nearly gave up ...and really struggled as she didn't expect to be so homesick. BUT by the end of the year she was making friends, in her 2nd year she found her soul mates and after that, had a great time. This was the girl who had never been ancious in her life, before!
DD2 was also very very homesick..and missed her sister terribly. At one point when she was really low I said 'come home.. forget Uni..we can figure it out' and it sparked the stubborn streak that got her through. she has now just taken up her first nursing post, in a new town, in a flat by herself (didn't want to share after 3 years of student living!) and she is coping :)
Freshers week is shit.. it really is. Full of scared young adults who are supposed to be having a great time, but a huge number wish they were at home with mum and dad, and familiar life. Once Uni starts properly, things start to slot into place. Gradually you will find people you 'gel'with and it will get easier...