Why is my new kitten sick with diarrhea? Is it contagious to my child?

Thank you for using Petco Pet Education Center, formerly Petcoach! Kittens may have diarrhea and low energy due to a number of conditions including intestinal parasites, viral infections, or a change in diet. I recommend having both kittens examined by a vet as soon as possible, as it is likely that the condition is contagious. To speed up the diagnosis, I recommend bringing a stool sample from the sick kitten in a disposable container for your vet to check for parasites. It is important to have the sick kitten evaluated as kittens can quickly become dehydrated and have low blood sugar, making them feel even worse.
While it is unlikely that your son got sick from one of the kittens, it is possible. I recommend that you have him seen by a physician if you are concerned.