You should try to talk to a doctor or psychiatrist about this habit, especially if it's beginning to bother you and affect your life in other ways.
As for things you can do right away, how about sticking bandaids on your sores, this will help them heal and it'll also keep you away from the area. And don't wait until it gets bad, but even put bandaids on prematurely if it'll get you to stop compulsively messing with your skin.
Another thing is to buy some basic skin care tools. As someone who has the habit of biting my nails, sometimes until they bleed or are painful, I know that biting them can lead to making them rough, which just leads to making me even more compelled to bite the rough bits. For me it can really become a cyclical problem that's also likely driven by anxiety and depression. But by clipping and filling my nails with proper tools I can quickly break the cycle, because my nails will start to generally feel better. So maybe you can do something similar with your skin by exfoliating and using lotion! It's worth a try!
Finally I want to say that cannabis has been good for my personal type/level of anxiety, though I hesitate to recommend it because when though I don't find it addictive I think it maybe isn't great to recommend to someone who is experiencing addictive or compulsive behavior.
In the end I think some combination of therapy, behavior pattern breaking and maybe drugs if necessary, might be able to help you get away from self-harming compulsive behavior. Good luck!