If the pink goes evenly all across her whole belly I would say it looks like pre-shed (which also matches her behaviour of staying in her warm hide and not being very active when taken out) but since OP mentioned it's only on the part of the snake near the tail then that makes it more likely a burn.
Very lucky that you checked on her today as you probably stopped it from turning into a serious burn and it looks mild right now. I don't think there will be any long-term damage, and it will heal up completely after a few sheds. I have no experience with how to take care of burned snakes so I can't advise on that but I'm sure someone else will have some good tips.
For the UTH situation, the probe should be outside of the enclosure, between the heat mat and the bottom of the tub. This is to avoid the problem of the probe being moved, causing a UTH temperature spike. You can try very carefully peeling off the UTH, taping the probe to the bottom of the enclosure, and taping the UTH back down on top of it with foil tape. If the UTH gets bent or damaged in any way while removing it though it's safer to just get a new UTH.
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