If you have any mesh in his cage, he might have rubbed his nose against it (or even rocks, etc). Else it's possible he might have burnt his nose on whatever heating you have. This seems more likely if you're using lights to heat his cage. I'm fairly sure bathing burns is bad and can open them to infection?
It's very important your pet sees a vet right now. There has got to be other vets? Called around perhaps?