No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Was the loan still held by Sallie Mae? If they sold it to a collection agency, reporting by Sallie Mae would only continue for 7-7.5 years after the date of the first late that led up to the default. Is the CA that currently holds the loan still reporting?
I'm sure that your score increase is related to a negative account being removed - defaulted installment tradelines cause a significant hit to your score.