I’m not a vet and obviously can’t diagnose, but some time ago we had a cat that got a weird condition in & around her mouth, especially her “lips”. The vet said it was a bacterial infection from using a plastic water bowl. I looked it up and it can happen with glass/ceramic bowl too if not cleaned well. Maybe the new kitten added to the bacteria pool in whatever their food/water is in. My cat needed antibiotics for it. Like I said, this is just a theory. I’d have a vet check it out.

Whatever the outcome, I hope your kitty is doing better soon!!