It could be stress related by the addition of a new pet. Especially if the pup is invading her personal space. But it also could be an indication that something is going on physically. Is the kitten spayed yet? I know when I had one cat who wasn't, that started when she went into her estrus. She seems very young to have bladder/kidney issues but ruling it out is not a bad thing to see if it's physical problem.

Also make sure the puppy isn't preventing her from using her litter box (I assume she's an indoor cat). Set up her litter box, even if you have to use a baby gate, so that she has her own private room. I'm sure at this point she is missing the peace and quiet she used to have.

Here is a link that might be useful: Gate