Two days ago, a stray cat was in my yard and as I went to go pet it, it latched onto my arm and bit me. There are two small holes, one near is near my wrist. I have been cleaning it every morning with peroxide and throughout the day it stays red and sore. On a scale the pain is almost a 2-3, kind of like a bad bruise or arthritis. Any suggestions?

Yes, see a Physician - for starters you need to make sure your tentanus shot is up to date. I'm a liability investigator - I've seen horrible, horrible infections from animal bites. This was a stray and many different disease/health factors could be at play.

Get this treated by a medical professional.

... and to add to what Judy said... Let this be a lesson to you. Strays are not always that friendly. I learned the hard way when I was a kid and went to pet a dog. Now, if I don't know the animal, I keep my distance.