Oh, I'm sorry to hear about your daughter's picking.
You are right to be concerned and to seek the input of a professional. It's important to rule out medical conditions.
On a personal note, my youngest daughter was severely burned on her hands when she was just a baby, about 1 yr. old. Her palms had 3rd degree burns. It was beyond horrible and required hospitalization and weeks of trips to the burn center. She developed a habit of picking her fingers down to the layers you describe. And I couldn't believe it did not hurt her. A therapist helped me understand that it did not hurt as much as the original burns.
On a positive note, I also learned that it is typically very bright and smart kids who will develop these odd little habits. She is now 10 and her fingers are not perfect, and during times of stress her picking starts back up. And when I notice it I spend a lot of time talking to her about her feelings, what is going well, what is frustrating. And then we pull out the pretty nail polishes and will paint pretty designs or patterns that she chooses. BTW, this is huge for me as I don't do my own nails. I'm not a nail person at all, but I do this for her.