How to change my iPhone back to iOS 6.1.3?

I did all the steps to get the iOS 7 update for my iPhone 4S and it was working fine until I accidently synced pictures I didn't want onto my phone and it wouldn't let me delete them so I reset my phone. I keep selecting the language and everything then it pops up saying it's activating my phone and it doesn't. It says I need to be part of Apple's developer program and I really just want to put my phone back to normal. My sister's was doing fine but my phone is just messed up now. It doesn't want to connect to iTunes and I can't reset it back to iOS 6. I don't know what to do I'm really confused and lost, I can't get another phone. I really regret messing with it, I should've been patient and waited for the actual update to come in the fall. If anyone knows how to fix this problem please please please answer!

Best answer please?