Alright, so based on what everyone was saying, I did a little searching of the AT&T website. I found a feature where you can add names to a list of 'Retail Authorized Users', which means that if you're on this list, you can make account changes in AT&T retail stores. Along with adding my name to this list, I checked and made sure that my name was already an Authorized User/Primary User (on my line). I'm still going to go to my Apple Store, and hopefully this should all work out. Thanks for everyone's help!
EDIT: I just found this under the Retail Authorized User link: Retail Authorized Users and Apple Stores - If visiting an Apple store, the primary account holder must be present. I have to call Apple or AT&T tomorrow. This is frustrating.