I don’t have experience with crayfish, but I used to have pet crabs. Occasionally they’d have an issue with molting (stuck in their shell, losing a claw, can’t get skin off etc). If you feel the piece that’s not coming off and it’s loose, you can gently help it come off by running the pad of your finger over it in the direction of the molt. If it is hard stuck though do not pull it as you can do more damage. If one of my crabs couldn’t get a piece and it was beyond my help I’d generally let them figure it out. They sometimes would have to regrow a claw or rub against something and get it off on their own.
To address the shell rot, you should see if there is a recommended medication that can help her heal the damage. That could also mess up her molting process as it could be painful and she could be avoiding trying to molt naturally. (I know my crabs would sometimes just pull pieces off that they could get to, if she does the same she might not want to if the shell rot is bothering her too much). I don’t know how to diagnose shell rot, so this isn’t me confirming she has it or not, but if that is the case you should confirm it and treat it so it doesn’t spread