If a cat or kitten has ringworm then they do not necessarily get over it quickly. The stress of relocating to a new home is enough to trigger a relapse. As you mentioned, best thing is to take the kitten to the vet.
For yourself, you are either going to get it or not. I have been exposed on multiple occasions yet never had it while I know others who get it every time they come in contact. So some people are susceptible and some aren't. If you notice spots appearing like little ovals then you have developed it. It can appear over a week after exposure. Should it appear then the best bet is to see your family doctor for an ointment and cover the area with a bandaid so that it does not spread when you are wearing clothing that can rub it.
"For every animal that dies in a shelter, there is someone somewhere responsible for its death".