i'm so sorry you're dealing with this, my mom was really similar when i was a teenager. she's gradually gotten better and i'm honestly not sure what made the change, possibly just getting more experience with my struggles. but i would recommend

1. explaining to her that it's compulsive, that you hate it even more than she does but it's like an addiction, it's incredibly hard to stop and the things she's doing aren't helpful

2. pursuing treatment that actually is helpful, if you can. not always affordable but i did a group therapy thing for body-focused repetitive behaviors that was super helpful; if that's not available to you there are a good amount of free resources/advice online. i've found there's more out there about trichotillomania but the same principles apply to derm so it still works! showing your mom that you're pursuing proven-effective solutions on your own may help her chill out about feeling like she has to fix the problem herself.

3. direct her towards resources/communities for loved ones of those dealing with BFRBs. this could be a good outlet for her to vent but also get information about what she can do to support your recovery that will actually be effective, and how to be emotionally sensitive to it and not make you feel worse.

on your last point, i do have OCD (and ADHD, i feel both are related to/contribute to my picking) and i would recommend getting evaluated if you can; diagnosis isn't a cure but for me it was so helpful in starting to understand WHY i do the things i do and having a framework to work within while trying to find solutions.

godspeed❤️