Welcome to the site!
Hot side = surface temperature if you are using a UTH, cool side = ambient
The hot side probe should be on the floor of the cage centered on the UTH. Where is your thermostat probe?
The thermometer/probe on the cool side doesn't matter as much as long as it is on the cool side.
I would suggest that you try to wash some of it of, you need to know what is going on with your snake. The stress induced from a quick dip isn't as bad as letting things get worse. If it is a burn or scale rot he will need to get to the vet ASAP for treatment.