Eliza, you do apply seperately for non-government loans. You can borrow from the government up to 18,500 per academic year (8,500 subsidized & 10,000 unsubsidized). This I'm sure you're familiar with.
For outside loans it's a little different. You first need your total cost of attendance. This number can be found by calling the financial aid office at your school. From that total cost of attendance number you subtract the 18,500 and also any outside aid (i.e. scholarships, grants, etc). The remaining amount is the total amount you are allowed to borrow for "non-government loans." You apply for these on your own through many different sources. Sallie Mae, Nellie Mae, Citibank are some of the large ones. You may also borrow from a bank such as Suntrust, Wachovia (highly recommend since I work for them), Bank of America, etc. The interest rates and fees on these will vary by the lender. There was a thread discussing lender options somewhere, I'd run a search.
And In Vino is correct, carrying a balance on your credit card isn't necessarily a bad thing. What you want to do though is make sure you are making payments on time as In Vino noted, but also make sure your balance on the credit card is less than 50% of the credit card limit. If it is over this will hurt your credit.
Hope this helps, good luck.