You've said repeatedly she has diarrhea. Probiotics help treat that. It doesn't matter if its from IBD, or a food intolerance. Probiotics are crucial to cats with IBD, but even cats with diarrhea from a food intolerance benefit from probiotics. It's likely that because she's young, she just gets diarrhea when you change foods. It's incredibly common and it doesn't mean she has an intolerance, but we don't really have enough info to know one way or another. Probiotics can help make adding wet food easier. Wet food is very important for cats to eat, ideally you want to feed all or mostly wet food.Everything Ive read about probiotics say they are for kitties with soft stools and diahrrea, and ibs. Neither of which Lilly has...
As I've already said, I give them daily to all my kittens to help their immune system and help digestion, even though they don't have any soft stool issues. Here's another link if you need more info. If you're still confused contact your vet and ask what they might recommend, most vet's use and recommend at least some kind of probiotic.
http://www.foodfurlife.com/use-probiotics-in-cats.html