Considering dropping out of University? Watch
You've come this far, its your second year, personally, if that was me, I would just go for it. Have you tried talking to the student support services thingy? I'm sure they help you with this type of stuff and give you guidance or something. It's definitely worth it if you keep going, you've got nothing to lose. I think the distance is having a bad effect on you, is it too late for you to transfer to a different uni for your last year?
I guess it depends how badly you want to become a psychologist and whether it is worth battling on through uni to make that happen.
Are you lonely at uni? Nobody can replace family but to be that homesick in the second year suggests that things have maybe not worked out socially for you.
Talk to your university about how you feel. Maybe they can help. I think you need to get to the root of why you feel so unhappy.
I'm not going to give you the usual BS 'join clubs' advice. If you can't improve the situation where you are then perhaps try to transfer somewhere closer to home.