Toddler Face Picking

My daughter is 27 months and sucks her fingers. While sucking her fingers she rubs at or picks at her chin. She just recently started picking at her chin till it bleeds. There are no signs of a rash.. she seems to do this out of habit. Once she tears the skin we put a band aid on the area until it heels... but once it's heels and the band aid is removed she is back at it again. This has been going on for about 4-6 months and has gotten worse. Plan to check with the doc... but wanted to know if anyone here had any input ?