I would first call all the vets in your town, and see if they can see you for an emergency.
i've never delt with scale rot or a burn, my question really is how often have you handled her lately? that looks like its been in the works for a few weeks.
but either way, vet asap.
as for the UTH, make sure you're regulating it, it would make sense if she got burnt and now is shedding so quickly after the last