5mo puppy peeing constantly?

Disclaimer: we've been in touch with the vet and told to keep an eye on her, but we're looking for insight/moral support.

Our puppy is just short of 5 months old and is mostly potty trained -- if she has an accident, it's because we've missed her cues. This morning she's had several small accidents, tiny puddles she won't even try to warn us about. She tried to pee last time my husband took her out, but that didn't work.

We're obviously suspecting UTI and are a bit frustrated that we were instructed just to keep an eye on her for the rest of the day. Her butt is constantly wet. Is there any way we can help her feel better in the meantime?

Another issue is that she vomited a clump of fur this morning before her breakfast. She's been licking her business a lot, so we're worried about a possible blockage. She did eventually eat some of her breakfast and we're watching her like a hawk now to see if that comes up too.

According to the vet, the licking could be related to a heat cycle and she could be displaying early signs of heat even though she is only five months. I read up on heat symptoms and so far the only applicable ones have been the genital licking and frequent urination. (There was some reddish discharge on the snow around her yesterday, but she's teething right now so that's probably the more likely cause of bleeding.)

Behaviour-wise, she seems herself, not particularly under the weather or lethargic but clearly weirded out and uncomfortable.

tl;dr: Puppy urinates constantly, licking herself, loss of appetite, puked up fur; we can't decide whether we should be worrying about UTI, blockage or heat, or all three.

ETA: this is her enjoying the snow yesterday.

ETA2: she has UTI and is being treated now. Hope she's on the mend soon. ❤️