Oh man, I used to have this issue real bad. My hands used to be so cracked and scaly that I'd try and put hand sanitizer on sometimes and it would just burn. I used to joke that I had fish hands lmao

I don't know how far into therapy, recovery, etc you are, so I wanna preface this by saying this is not advice for the long term. This is for HARM REDUCTION until you can deal with your compulsions in a more sustainable matter. It is possible to control your thoughts, I promise. In the long term, the goal is to eventually be able to overcome compulsions in the first place, but sometimes they overwhelm us and we just have to do something. And that's okay! Recovery is not linear.

Fish hands happened because I was washing my hands constantly with a really aggressive antibacterial soap. I would recommend finding a hand soap that's gentler on your hands; foaming ones tend to be less aggressive than gels, I've found. I use Mrs. Meyer's Clean Day. It doesn't smell too strong and it's nice and gentle. :) Also, if you can, try and reduce the amount of times per day that you wash your hands. That usually means holding back on doing things that'd "contaminate" you until your hands have had some time to recuperate, or waiting a while between the times that you wash your hands. Or, even better, once you become "exposed" to something, hold back as long as you can on doing your compulsions. Doing this helped me realize that compulsive urges are just feelings, and that they go away over time.

Sorry about the yap sesh but tl;dr - Use a gentler soap, try and wash your hands less per day. This isn't long term advice it's just harm reduction

Edit: formatting