I'm in the same boat you are. In college for the degree now. I'm working full time for a company, doing web related things, trying to get my foot in the door.
However, I am still trying to market myself as an individual web designer on the side. I have done about 6 or 7 websites on the side for clients - this is basically freelance design.
Once you graduate from college, you can work for a company, or do it on your own, or start your own business. It's really up to you what route you want to take.