Broken arm? Soon to die?

Question
I got given a baby rabbit tonight, and it had been attacked by a cat and barely alive then given to me to take care of it. She was barely moving, would not eat. Had to check various times to see if she was breathing her ears were ice cold yet she was still alive. Then i checked for her injuries. It looked like her back got skinned and there was one deep puncture wound. I cleaned the wound by using water and peroxide. While cleaning the very calm bunny freaked out jump straight out of the sink and onto tile (3 ft) right on her side. It looked like she was stuck couldnt get onto her stomach. When she finally got on her stomach she ran around the small bathroom not using her front right leg and losing balance. (The only reason she wasnt brought to a vet was because i got her at 12:30AM) is it time to give up and let go or is there anything else I can do?

Answer
Hello there
it seems like you have done your best to help.
you never indicated how old the bunny is.
or if it is a domestic or wild.
Where is the mother?
If the bunny is old enough to eat & drink on its own keep clean water available& some dry grass.
NO LETTUCE!!! carrots ok.
good luck