I've never had a bad burn so I have no experience with that kind of pain, though I would believe myself fortunate, as my guess is it's nasty and makes finding a comfortable position to sleep in difficult. I hope you're getting good medical attention and keeping it dressed correctly.
Hydrocodone has always helped me sleep, as I believe it does most, but sometimes meds can have opposite effects for some people in some circumstances. Sorry this finds you there. Hydrocodone does have a tendency to slow bodily functions, so 2nd Wind's recommendation of prune juice should not be ignored if you notice infrequency in that area.
You should probably visit with your doctor about pain management and sleep, and buy an air conditioner.