Skin picking

My daughter (three) has been picking her face since she was (one). She only does this when she is sucking her fingers... Mainly when falling asleep ...or bored. I asked her why does she do this to her face and she said because she likes to. We took her to the pediatrician because the picking has become so bad that she is causing her skin to bleed and leave scars. What you see in the picture below had occurred over the last few days.. the pediatrician suggest that we see a dermatologist... her skin Is not dry. My question is. Have any of your kid(s) done this? Any suggestions 😔😔😔?

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