I can't help with the mouth rot, but would suggest a vet visit soon for it. Here is help with the shedding problem, including prevention:
To prevent problems with shedding, it is important to maintain higher humidity than normal during shed cycles. If you are using a glass cage with a screen lid, you can cover 1/2 to 2/3 of the screen lid with plastic or plexiglass to keep the moisture in. You also might want to provide a humid hide, which is simply a container of the correct size filled with moist spagnum moss that the snake can enter and use as a hide. Cut a hole in the side and keep the lid closed to maintain the moisture. Apparently, heat lamps can dry out the air in your cages, so switching to an undertank heater can be helpful.
If your snake has started to shed, but has patchy unshed skin remaining, take a plastic animal cage, such as the Kritter Keepers, which are sold by pet stores and animal suppliers, of an appropriate size. Make sure the container is secure! Nothing is worse than finding that your snake has escaped the container. Put about 1/2 to one inch of warm water in the bottom. Then put several paper towels in on top of the water. Put the snake in there. Then put a few dripping wet paper towels on top of the snake. Leave the snake in there for about 30 minutes. Check to see if the snake has completely shed. If not, put the snake back in for another 30 minutes. Repeat as necessary. I have also heard of people using small towels in these containers. The beauty of paper towels is that you can just throw them away instead of having to wash them. You can also take a wet sock, for a small snake; or a wet pillow case, for a larger snake; and put the snake into it, secure the top, and put the whole thing into the snake’s cage overnight.
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phflame
kingsnake.com host