This cutie followed me inside. I think I got a cat?

Bit early to tell. Better make sure he/she doesn't belong to someone else first.

Please take them to the vet and check for a chip. They'll usually do this free of charge at reception where I'm from, not sure about where you're from.

Has he taken a nap yet? If not, he's just visiting.

what a beautiful face

I believe you are confused: That cat might have gotten a human. You belong to him/her now, human.