Could this cat have rabies?

2 weeks ago i saw a kitten next to a shed in my neighbors backyard i came up to it and it sat completely still so i picked it up and i started walking back to my house and the cat bit me on my finger i had dropped it and it ran under some bushes i went home and washed of the bite with soap and water for 2 min and poured some hydrogen peroxide on it and put a bandaid on it later that night my dad noticed the cat that i told him about and he went after it and it ran under the neighbors car my dad pulled the cat from up under the car and we took it home to my mom and she gave it a flea bath and noticed a bunch of red spots on its belly from fleas and after giving it a bath my mom kept it on her bed with a heating pad and it did nothing but sleep for 3 hours straight so my mom woke it up and tried bottle feeding it and it would eat some but kept spitting the bottle out so my mom let it sleep for the night and fast forward to the next night and the cat had diarrea it wouldnt eat and was just sleeeping and it died and before it died we also noticed that it had white paws and gums do you think it had rabies???