T.,
I had a son, that about the age of three went through biting. I was as upset as you.
What I finally ended up doing was either putting the stuff to stop thumb sucking or a bit of vinegar on his tongue every time he did it. This did not hurt him, but he soon associated his biting someone with something very unpleasant for him. (I just couldn't bring myself to bit him.) He stopped within weeks.
Something else you could try is to explain to your daughter, quite calmly, that if someone did the same thing to you as was done to her, you would do this or that and explain how you feel this would help. In this way you reinforce positive actions without criticizing her or getting her to react negatively. Some kids are very sensitive at this, or any age. This way you put more appropriate options in her little head without making her feel she is the "bad" one.
Good Luck