10 Week old kitten has diarrhea and is vomiting?

I agree partially with the person who said it could be coccidia. It could also be the stress of changing environments and foods has caused an overgrowth of bacteria in the gut. Either way, a round of antibiotics should clear it up. Yellow throwup is basically bile, meaning the cat is tossing on an empty stomach. It's not going to clear up without antibiotics, though, so please get her into the vet.