Three year old picking?

My three year old has been skin picking since she was 17 months old. I have taken her to see five different doctors since it started. Finally, after a year of being prescribed emollients, had two failed referrals to dermatologists (I have no idea what is going wrong, but the referrals are seemingly disappearing), a very lengthy and drawn out email back and forth just trying to get a call back from a private paediatric sensory psychologist (which I gave up on when nobody ever got back to me to actually discuss the issue no matter how many times I called or emailed), I have all but lost hope. I just don't know what to do any more. She picks/scratches idly throughout the day, but it's so much worse at night. She woke up this morning with about a dozen fresh abrasions on her chin and cheek. I'm at a total loss as to why she's doing it and how I can help her. She's had impetigo a few times because of it and it always looks so, so sore. I've taken to the internet a few times to find out more information about why she could be doing this and how to help, but it's my understanding that this is quite uncommon behaviour in someone so young, and taking her to the doctor is the best course of action. Which brings us full circle! I feel like I'm banging my head against a wall. She can't be the only one? Has any one got any information or suggestions of what to do/where to turn next? I'm starting to find the whole thing quite distressing, especially as every time I seek help it seems some higher power is conspiring against me to stop me from finding any answers. Thanks in advance.