Taz bit me before (not the first time ) and I didn't do much to it except wash it with anti-bacterial soap. A few days later I felt a pain on that finger and thought I had a splinter or something, but there was nothing there except what looked like skin peeling. I eventually realized that was were he bit me. I put peroxide on it and it stopped hurting right away and was gone quickly.
But I'm not a cat bite expert. Only telling you my experience. And I'm not a child either. But I know that when I was little my mom would just wash it out with peroxide and we'd be on our way. I grew up with dogs and cats that lived outside (yeah, I know ), so they probably had all kinds of germies.

I hope Tyler's bite doesn't get worse and all is well soon.