How can I get turned down for law school student loans?

Last year I was awarded with student loans for law school, but two months ago I went over my credit limit (once) on one credit card, and then I went over my credit limit (once) on my other credit card. I cleared this up immediately, but it's still on my credit report. Could this get me turned down for student loans (both governement and private)? If so, is there anything I can do about this, other than get a co-signer?