R.
My little sister did (probably still does) the same thing. I can't remember at what age she started it but I thought she was a little older than 4. I know my mom tried bandaids as well and they didn't work either. What seemed to have some impact was that my mom asked my sister what would be something she really wanted to see/do. My sister really wanted the family to go bowling. So my mom said that as soon as she allowed all of her sores to heal we would go. I remember how excited she was when it finally happened. I believe she still picks on occasion but it isn't to the degree that it was, she is now almost 12 and I think she cares a lot more about her appearance.
So my advice is that you may want to try some sort of reward program.
Hope it goes well!!