K.T.
One question I want to ask is if your daughter is talking yet or has any issues with speech. Often children will bite or hit out of frustration because they can't express themselves and get their needs met.
Try not to react too strongly to her doing that because if she sees that she has some control over your response, she may do it more simply because children of that age are beginning to assert their independence and they want to find ways to control their environment.
My daughter used to hit herself when she got angry over being redirected or not getting what she wanted. It took some time but she eventually stopped doing that since it never gave her what she desired. It's hard to watch, but if it were to become severe such as drawing blood, you could certainly take her to her pediatrician to get her checked out for sensory issues but don't diagnose her yet. It may very well just be a phase to express her frustration.
Another thing you could do is learn the signs of her getting frustrated if that's when she bites and give her something else to hold or bite into.
I hope this helps. I know how frustrating something like that be. No parent wants to see their child do something potentially harmful to themselves.
K.