Before you assume depression consider that you are homesick and used to having everything done for you. A gap year is supposed to be fun. Not misery. Whatever possessed you to go by yourself? Mistake one.
Before seeing a doctor I would consider going home. Can you not at least live separately so you can party and have real friends there too?
The problems you describe are self inflicted and I'd suggest it's just ego/pride stopping you going home. Just tell them "I can't do it right now" and go home. They'll welcome you I'm sure.
I assure you going home and settling is much, much simpler than going the doctor/meds/therapy route only to find out you want to go home. By then it will be a habit and yourt life? Who knows, mayvbe screwed by then. Go and do it now.