How do I get her to stop picking?

My 2-year-old got some pimple-looking things on her face at the beginning of the month and she picked at them until they were bleeding. Now she keeps picking at the scabs and newly formed skin, and the sores won't ever heal. I'm worried she's going to end up with scarring all over her face after this. I've tried bandaids and they worked, but after now she won't let me anywhere near her with the "stickers", as we've been calling them, because she learned they hurt coming off. Any ideas how to save my poor girl's face?

This is how she woke up. She has a lot of dried blood covering her face, like the bit up by her eyebrow. Her sores are on each cheek, her chin, and her nose. UPDATE: I took her to the doctor, and they gave her an antibiotic in case of infection. They also suggested benadryl to help in case the sores are itchy. And I let her pick out some bandaids that I'm hoping she'll actually use. UPDATE AGAIN: she actually let me put "stickers" on her face last night!

They're already looking better. Now to keep her from constantly picking throughout the day.