Paying it off immediately wouldn’t help your credit score. You’re better off to try to refinance to a better fixed rate. I know that typically college loans can be financed at pretty low rates. I know that my wife was able to get hers down to 3.4% or something like that. That was a few years ago so obviously it would be higher than that.
I’d also suggest you use your credit card regurarly. As long as you have self control it’s actually a good idea to use a credit card. We have no annual fees, pay it off every month, and get cash back. If our minds, we’re actually making money from the credit card company. Plus it looks good on our credit.
I agree though, the credit world is very tricky. You’ve got to have credit to get credit. I’ve always joked with my parents that they’d have trouble getting a loan.. house is paid off, pay cash for cars. It’s definetly good to have at least some debt constantly going to prove you can make payments.