I probably would be stubborn and not go to the doctor, but just keep it cleaned out with peroxide. Although, I've not been bitten that bad before. Once Taz got my finger and I didn't do anything about it and it began to hurt like I had a splinter in it or something and was red and puffy. Once I remembered that he had bit me there I cleaned it with peroxide a few times and it went away.
But like LeahMM said, cat bites are bad. And with the severity of yours you might want to seek medical attention asap.
The only thing that scares me about that, is usually the doctor (at least here in Cali) have to report it to animal services or what ever.
I hope you feel better soon.