I remember going away for a couple of weeks when I was younger and got really homesick. Afterwards I looked back and thought it was daft, because after I'd returned home I realised I was actually away for no time at all.
So when I went off to college I went with a different attitude. I knew I wasn't going to be away for ever, and although it was a bit strange at first, and it was a bit daunting going somewhere you know virtually nothing about (certainly during the first 10 weeks anyway), for most people it's a fantastic experience.
You get to meet TONS of great people, you get a freedom, and personal responsibility you've never had before living at home, and I know that throughout the three years I was at college, I grew up immensely.
In the end I suddenly realised I wasn't homesick at all, and although it was nice to go back home in the holidays, I looked forward to getting back there.
There will be times you feel bad, but if you refuse to worry yourself sick about it, I guarantee there'll be many more better ones.