Hello!

Last Sunday (May 24th) my two year old unvaccinated outdoor cat bit me after I was going through my drawer. It was unprovoked, but this has happened before. This time I felt like something was a different though. I mean he bit and scratched me, but the bite didn't break any skin and there were only three scratches. I watched him over a 10 day period since Sunday, he's been eating, drinking, and sleeping normally until yesterday when he came home with an infected eye. I let him out during the 10 day observation because he was unwilling to stay inside, so I'm not sure what to think. He still ate and drank with the infected eye, but kept constantly itching it and falling over doing so.
Behind my backyard is a farm where skunks, raccoons, snakes, and horses live so i'm sure he has fought with those animals. He even fights with our neighborhood cats, which caused me to think he could have been exposed to rabies. Also, he usually returns home in the morning, but this morning (10th day) he hasn't come back since. I'm not sure what to do, I feel like I should visit the doctors to get vaccinated, but he just didn't seem like he was rabid at all. He's attacked me before on multiple occasions, but this time I've just been stressing over the possibility of me getting rabies. I also have what looks like a bat bite on my arm, but i'm not sure because I didn't see any bats in my house, but I do have many big holes in the wall. I feel like I'm being a hypochondriac, but it's never a bad thing to be too safe. I'm just scared and need advice!
I live in West Jordan, Utah as well, so I'm not sure if there are many bats or cats with rabies, but it's always possible.
I appreciate your guys' time and just need all the insurance i can get right now.