How long since you fed him? I would give him till the morning and them feed him a tiny bit, ie one flake. It could be a parasite, a blockage, or a dozen diseases we know nothing about. Epsom salts can help with swelling.
He had one small pellet (not a betta pellet, but a regular fish food pellet) last night and before that he had his regular "meals" on Friday. He ate just fine then.
Also, I don't want to move him from the 10 gallon to the one gallon because I'm affraid it would stress him out too much. If I did an epsom salt bath in the tank he's in now, would it be safe for him to be in there after about 10 or 15 minutes if I did a partial water change?
Just an update. After a long fight and trying hard to make it, Magellan passed away early this morning. He will be greatly missed and was a wonderful fish. I'm just glad he won't be suffering anymore.
Thank you all for all of your help and suggestions and well wishes. I appreciate everything everyone did to help us!