I took Squeekums to the vet after work, and he said she's definitely got something going on there. He said it could be either of two things--a urinary tract infection, or it could be minerals crystallizing in her bladder, causing inflammation. The symptoms are the same, and the only way to know for sure would be to get a urine sample. To do that, they'd have to sedate her and run a catheter up into her bladder. But, since the treatment for both is the same, he wasn't going to do that just yet.
He gave her a shot of antibiotics and some anti-inflammatories. He also sent home some prescription cat food that was specially designed to dissolve any crystals that may be forming in her bladder.
Of course, if she's not better in a few days, he said to bring her back and they'll pursue the matter further.
While I was there, another person was bringing a dog in (a small dog). He didn't have the dog on a leash, and it ran away. Several of the workers in the clinic ran out to help the guy catch the dog, and they probably scared it even further. They eventually managed to catch the dog, but they were very lucky. I mentioned to the receptionist that I would never take my dog anywhere without her being on a leash. When they get into an unfamiliar situation, you just never know what might go wrong.