Hi Michelle,
Because you have a short credit history, you haven't really had time yet to prove yourself as a responsible borrower. That's great that you're paying down your cards so quickly and have a $0 balance on most of them, but new lenders might still worry about your potential for maxing out all those cards. In your case, I would say closing a few of the retail cards would be okay. But that won't mean you'll be able to turn around the next day and get approved for that mileage card you want. It may take a few years to establish some solid credit history before you qualify for anything new, and just because you cancel credit cards doesn't mean they fall off of your credit report immediately. In the meantime, keep paying down your balances so you avoid paying interest, and don't apply for any new cards. At the cash register, when they tell you you could save 10% today by applying for a store card, just say no! Out of curiosity, have you checked your credit scores lately? That would be another good step you should take.