Bitten by a cat last night, didn't think anything of it.

I am a 23 year old female, last night I was out with a friend and when we got back home her cat bit me. I didn't think anything of it and was fairly drunk so just went to bed. Today the wound still hurts quite badly, it bit me on the finger - one tooth went into my cuticle and the other went into the skin between my nail and finger. The area around the bite is red, hot and throbbing with pain. What is the likelihood this means it has got infected? Or is it probably just painful because of the bite itself? Thanks!