This is kinda nutty, but I read once you can substitute the cutting for something else. One suggestion I read was to put band aids all over your skin in the places you want to cut. I imagine drawing on your skin in those places would be the similar. I realize these are strong urges though. Just tossing this out in case it helps.

Do you have a friend or family member close by that would let you use their shower? It must feel awful not being able to get clean when you want to.

I'm sorry you are going through this.