zanymom-Take a deep breath. Try hard to realize that you are human. This acknowledgement has been a big one for me as a first-time mom. I thought I had to be super human, never get angry or frustrated or tired.
But biting HURTS. My DS (2) went thru a biting stage. It is now over. I yelled more times than I want to admit, but pain puts me over the edge. I always apologized for it, but also acknowledged that I was angry.
Try to go easy on yourself. It's one thing to feel guilty, yes, we all have reactions that we aren't proud of sometimes or that we just feel that we could do better. But try to distinguish that from feeling like a bad mom. The bad mom thing doesn't get you anywhere. It's like a shame thing. It just doesn't work for anyone. Just do your best, and when you don't, acknowledge it to you child and yourself and move on.
Best of luck to you.