Didn't know it had such a long name
I have also had this problem since I was a child. It began with bites, cuticles, etc. but as I got older I learned to pick selectively (bumps on my back or scalp where people wouldn't see). I've had my scalp such a mess that I was embarrassed to get haircuts and gave them to myself - not recommended.
Like you, I hoped stopping the drink would help (almost 10 months now), but it seems to be worse at times. Although my self-control was lowered by drinking, I find the need to pick is worse without my other means of dealing with stress. I've seen an improvement for several months (had to make a conscious effort to stop each time I found myself picking). I've recently found myself backsliding in the same ways I did with drink (just this one time, just until I get this particular scab off). I find that I have the urge to "clean" my skin of any roughness, loose skin, etc. as though I'm making things better when all I'm doing is creating a scar and causing infection/inflammation.
Helps to know others have this problem. Didn't offer any solutions but will do so as I make more progress.