I can't tell you how to get her to stop. This is similar to nail biting. It's a bad habit and so you and she will need to find an acceptable replacment habit.
I do the same thing, picking at my fingers. I set mini goals with mine. If I don't pick all week, then I buy a nice pen. Then the next week I set another goal; if I don't pick this week, I'll get a Starbucks. If I fall off the wagon, I don't beat myself up. I try to reflect on what happened - a big meeting, a big deadline, etc. Then I refocus, regroup and try again with another goal the next week.
For what it is worth they rarely get infected if that eases your worry any. It gets out of control when I am stressed. I would make sure she understands not to be ashamed about it. Shaming never helped anyone whether she is putting it on herself or perceiving it from you. I keep my hands moisturized and that helps with the rough edges Marie C. mentioned. Other than that I have to keep it in the forefront of my mind. Do not pick; do not pick; do not pick. At work it's the worst and the hardest to control. My mind is focused and I find myself with bloody fingers long before I realize what I am doing. My husband nags me which I detest so don't go that route. I don't need anyone telling me how bad they look; I can see that for myself. What helps me is finding a replacement habit and setting those mini goals. I chew a lot of bubble gum. My nephew does a similar picking thing with his thumbs. He found it useful to wear rubber bands which he could sort of pop when he was feeling the urge to pick or caught himself in the act. His hot button was school and it was similar to my work situation. You get focused, you start thinking hard and bam! you're picking. Good luck. It's a frustrating habit for everyone.