I know kids will chew on their finger, but I'm wondering if this is becoming a problem.

DD is a very "oral" kid. She has always needed to chew or suck on something to soothe herself (she would also rather eat crayons and chalk than play with it). If she doesn't have a paci or her blanket, she will have her fingers in her mouth. What concerns me is that she is chewing on her fingers, sometimes to the point of breaking the skin. It doesn't seem to hurt her, but it looks awful and she won't stop. I'm worried about infection, but I can't put a band aid on it otherwise she'll try to eat it.

Is there something I need to be doing to keep her from chewing on her fingers? Or is this just a phase like thumb-sucking?