Please don't beat yourself up over this. This stuff happens and the most important thing is that you apologised and talked it out with her. I think it is SO important that kids see that we are not perfect. And that we can mess up and admit it. She will now really understand that two wrongs don't make a right, ya know? I have found that these instances bring my son and I closer together, they don't create mistrust at all because I admit I did the wrong thing and we talk about what I should have done and he really enjoys being on the other side for a change - "You shouldn't have done that, Mummy!" In your case, maybe you could have just screamed in pain, really let her know how much she is hurting you? Ask her what she thinks you should have done to get her to let go.
I am just cringing thinking about how much that must have hurt!
I am just cringing thinking about how much that must have hurt!