I have an intense fear of rabies. Where I live there's tons of bats in the woods behind my house and I have found them underneath my deck before. I have taken myself to the hospital to get rabies shots after I *thought* I had an encounter with one

Earlier today I was over at a neighbor's house and I was petting their very sociable indoor/outdoor cat, when it suddenly bit me on the hand. There was no bleeding but the skin was raised and now there's the tiniest little red dot on my hand. I don't know if the cat is up to date with its shots and I didn't want to ask because I didn't want to sound ridiculous, but now I'm on a downward spiral because I've convinced myself I've been exposed

Prior to getting bitten my neighbors were telling me that their cat was getting over an eye infection, which they think happened after he got into a fight with another outdoor cat, and they gave him his eyedrops+medication while I was there - so I keep telling myself that the cat has been to the vet recently and the vet would make sure that it was up to date with its shots, but I'm still not 100% sure and now I'm sat here hyperventilating and in tears because I'm terrified lmao can someone talk some sense into me