Stray kitten bite?

My husband found a kitten last night on the road sitting by its mother who was ran over. She looked dehydrated and looked like she had a broken leg. We gave her water and canned cat food overnight and brought her in so we could bring her to a rescue group this morning. Well I got up and changed the towel in the pet taxi and she bit me and drew blood. She ped away later that morning. I have to say I felt relieved she was out of pain. I washed my hand real good and put Neosporin on it. I don’t know if she had rabies or not. My husband said no because she drank water. I just don’t know. she wasn’t foaming or drooling. She was wobbling but that was because she had a broken leg I presume. Should I go see the doctor? I am not experiencing any symptoms. Or will Neosporin help?