I've had 2 bad bites, and Tybalt has had two as well. All were severe enough to warrant antibiotic therapy, and one made me lose 2 days from work!
My first bite was from a friend's cat (spayed adult female) who I was catsitting in my house. It was my fault, I admit readily; she had gone under a chair to hide and I was trying to coax her out and reached for her. She bit my right thumb HARD and within hours it was swollen three times larger than normal. It took 2 antibiotics in combination to treat this.
My second was from Ulysses, who was semi-feral when we got him and had just been neutered. He had been acting sweet and friendly, I was petting him and let my guard down and BANG he struck at me like a snake and got me on the right hand, just below my index and middle fingers. I called the doctor and she called in a rx for antibiotics for me, but they didn't work and I lost the ability to move my fingers! I went in to see her and she put me on more antibiotics, and had me soak my hand in warm water with epsom salt for 3 days. That finally worked, and everything went back to normal!
Tybalt was bitten by a feral that we were helping to socialize, a scared, newly spayed female, and again by our sweet Ulysses.
By the way, Ulysses still does bite, but not as hard or as often. He likes to play rough and sometimes forgets himself... But all you have to do to get him to be the sweetest boy on earth is hold some food. He will turn himself inside out to convince you to give him some!!!