The earlier a child potty trains, the more likely she is to regress at some future point. I believe it's because the permanence of those "big-girl" demands hits her, and she longs for a more care-free existence, which may actually be a reasonable thing for a 2yo to desire.
The biting herself sounds a lot like my grandson whapping himself in the head at about that age – a practice that continued for almost a year. It seemed to serve two purposes. He got to express how frustrated he was (two-year-olds have many legitimate reasons to feel frustrated), and it got a reaction from the adults in his life, which gave him a little "hit" of real power, however negative.
We dealt with it two ways. We looked for ways to reduce his frustration (more "yes, you can!" and less "no, you can't," warnings when a transition was coming up, more choices, less rigid scheduling, etc.)
We also completely ignored the whapping. He kept it up months longer with a grandma who seemed shocked and concerned every time it happened.
I wouldn't insist that your daughter "love herself." To her, that could be denying her very real feelings and increasing her sense that she's not communicating her frustration well enough. If you talk to her during these episodes, try something like "You are so frustrated / mad! Can you say 'I am SO MAD?' Then we can help you find something happy to do!"
Good luck!