I have issues in my hands after showering. I tend to avoid washing my hands. What I do however, is wear compression gloves, at least on the worst days. They make them for arthritis, so that's where I looked to find them. The compression for my hands helps a lot with my hands not hurting with all the wrong sorts of sensory inputs that are going on.

Looking into Occupational Therapy, and in particular the Wilbarger Brushing Protocol would also be a good idea for this. Brushing isn't something you want to do without a professional however.

Sounds like that; yeah, it happens and is a common SPD thing. Earplugs or ear muffs at the worst times might help to start with. There are other things that can help, but they take more time.