I took her to the vet today. Singing to her did not quiet her down any in the cat carrier today, but she does seem to have a point when her voicebox wears out and she quiets down anyway. The vet's office wasn't a very long drive, though, so she didn't quiet down until we'd been sitting in the waiting room a while (with people staring at my mysterious cardboard box that was emitting high-pitched squeaks that didn't much sound like any identifiable animal species at all.
I took her out after a clerk called us in to an examining room. I showed her to the clerk, who dissolved into a puddle of cooing noises. The kitten purred at the top of her lungs. The clerk left, explaining that we might have to wait a while before the vet would be ready to see us. So we waited a while. The kitten was every shade of delighted, and continued purring at the top of her lungs. Eventually a nurse came in. There was no logical way whatsoever that a kitten should have been able to tell at first sight who was a nurse and who was a clerk, but the moment the nurse came in, she started very visibly trembling. Her purring, however, never paused or quieted down in the least. I think when we had been alone, she had been purring from happiness and relief, but there was no audible break whatsoever when she transitioned to purring from anxiety.
The nurse took her temperature and attempted to listen to her heartbeat. Later, the vet listened to her heartbeat too. Both of them turned on the water faucet as a way to get her to stop purring for a moment, because the noise of the purring drowned out the noise of her heartbeat. The moment the water was off, both times, she instantly resumed purring.
She didn't tremble so much with the actual vet as she had with the nurse. I think the vet thought she was purring purely from happiness, because he hadn't seen her trembling earlier. And maybe at that point she was partly purring from happiness again - but I think there was still some anxiety mixed in.
The vet adored her. The clerk and the nurse both adored her too, but the vet adored her most of all. He scratched her ears and swung her around in the air and held her upside down with her feet in the air and her head much closer to the ground than her tail, so that all the blood would rush to her head, and he said, "Look at that! She likes it! She loves being upside down!" And she did seem to; she didn't wriggle or make any protesting mews, and she went right on purring. So he did it some more, over and over, and exclaimed that "I can see why you wanted her!" (because she is a nonstop purring machine) and "I can't keep my hands off her!"
Healthwise, he said she has no sign of ear mites but that she's so young that she might not have signs yet even if she does have ear mites, and that she might have a mild upper respiratory infection (because I said she's been sneezing a lot, which she has) but that he doesn't think she needs any medicine unless it gets worse, because she wasn't sneezing in the vet's office and she has no eye discharge. (Upper respiratory infections in cats usually cause conjunctivitis, so the fact that she isn't showing visible conjunctivitis indicates that if she is sick at all, she's not very sick.) He seemed to think her fur was not quite ideally healthy-looking (I guess it's supposed to be more shiny and less fluffy - it looks fine to me though), but he asked me what I'm feeding her and then said "Oh good, that will give her healthy fur in no time." He said her incision from the spaying is a little swollen, but that it's nothing to worry about. Basically, she's fine.
And right now she has climbed into my lap of her own accord and gone to sleep.