I'm not sure it's a form of self harm.
Unless biting your nails is "self harm".
It's a habit, something you do for comfort, and usually without noticing you're doing it.
You don't think "I'm going to sit down and pull out my hair now."
You find yourself doing it when you are lost in thought. So times when you are preoccupied you'll tend to do it more.
It's not that big a deal. You've been biting your fingers until they were infected for years, but I'm sure you don't think it's a massive issue.
Listen to what she says about it. Does she want to stop? What kind of help does she want?
Something that can help with obvious bald patches is trying to get into the habit of twisting the hair at the bottom of the back of your head.
I am at my absolute wits end and in tears
I mean this in the kindest way possible, but you really need to get a grip.
How would you have felt if your mother had been in tears and at her "wits' end" because of your nail/finger biting when you were her age?
She has a habit that has unsightly drawbacks. It's very, very far from the end of the world.
Don't make this into a bigger deal than it needs to be.