Can my cat get sick from pumpking or from using same litter box as a kitten who has diarreah?

We found a kitten the other day she is about 7 weeks old and has really bad diarreah. Our vet said to give her wet food with pumpkin or yogurt mixed in it and to make sure she drinks a lot of water. We have another cat and she has thrown up and its definatly not the normal hairball barf that we get all the time, but she did get into some of the pumkin before she threw up. Her and this kitten have used the same litter box while the kitten has had diarreah. What I want to know is if this kitten could have gotten my cat sick or if it is the pumkin?