Does this sound like an infected navel piercing, and if so, how should I go about treating it?

Well, your piercing is fairly new, so you shouldn't be worried. Just don't use barred soap. If you're running out of time for school buy h2ocean and spray that on and inside your piercing. If it doesn't clear up in a week or so, it maybe rejecting so go back to your piercer and talk to them! Good luck :)