I hope that you are feeling better...wanna see a doozy of a cat bite?
My Razpy had gotten his tail caught under a door, and when I tried to dislodge him in my panic, I pulled the door when I should have pushed it and he bit me. This was on a Saturday. I washed it off, and then actually used a bleach solution on it, which can kill most things, but I wouldnt recommend that for your mouth!
I was working in a hospital then, and when I went to work on Monday and showed it to her, the ER director wanted to put me on IV antibiotics. (She said they could bring a pole to my office lol but I settled for pills!) I also got a tetanus shot. The pic is from the day I was treated, so the brown stuff is iodine solution.
What they worry about more than tetanus is cat scratch fever, and well as a localized skin infection. Cat scratch fever can be pretty bad if untreated. One hint an MD gave me (which wouldnt work for your lip) is that if you get a reddened area from a bit or cut, make a few light dots around it with a pen, so you can tell if it is spreading, which could be an indication of the infection getting worse.
Razpy has a heck of a set of choppers!