My son has trichotillomania (hair pulling) and skin picking is a related syndrome. Most likely the picking is related to stress/anxiety/boredom. Telling her to stop will not do anything because, as you said, it is a compulsion.
For trich my son had to keep a log. Every time he noticed himself pulling he had to write when, how many hairs, and what he was feeling so we could find the pattern. He also take the following supplements that seem to help him manage the urge. He takes 5 HTP 2x a day and a teaspoon of Inositol powder dissolved in juice 1x a day (sometimes 2x if he is feeling very stressed). The Inositol needs to be the powder not the capsules. He also used to carry around a small koosh ball to keep his hands busy.