C.C.
Hi R.,
My daughter didn't specifically do that when she got hurt, but she would have these major tantrums with hitting, throwing things, throwing herself on the ground kicking and screaming, banging her head into things, several times a day. In general she was a very angry little girl from the moment she turned 2 until the moment she turned 3. She pretty much defined the "Terrible Two" category.
Anyhow, although many people suggested to me that there was something wrong with her and that she needed everything from counseling to medication, I decided to stay the course with very, very consistent reactions on my and my husband's parts. Basically every single time she threw a tantrum, we did the exact same thing. We would very calmly lead her (or carry her) to her room, sit her in the middle of the floor, and tell her, "You can come out when you're feeling better." After anywhere from 2-15 minutes, she'd come out and would be totally fine, like nothing had happened. (Usually she would stop screaming after about 2 or 3 minutes, but she'd want to stay in her room anyway, and we would let her.) The point was never to punish her, but rather to let her get control of herself.
In short, I think emotional outbursts are pretty normal at this age. They just have no idea how to express anger, frustration, etc, in any other way. My daughter is 3.5 now and is back to her happy, perky self! Although she still gets upset whenever any little thing changes in her day (for instance if I pick her up from school, when usually Daddy does). Some kids just have a really hard time dealing with the unexpected. It is what it is.
Good luck. It is so hard at that age!