Verdict of the doctor: no signs of any bacterial infections in the various orifices, probably a virus. Come back if the fever isn't gone by Friday. She took a urine sample, but K isn't having any of her normal symptoms, so I would be surprised if it were the primary cause of all this (it wouldn't shock me if there were another infection brewing, since when hasn't there been one brewing in the past nine months?).
This evening, K napped on the couch next to me and I could feel the heat radiating off of her without even touching her. The immortal UTI aside, we've been extremely lucky with our childrens' health. Neither of them has had a virus last for more than a couple days or an infection that hasn't cleared up promptly with antibiotics. A case of bronchitis as a baby has given Alec reactive airway disease, which means he gets a couple weeks of wheezing every time he gets a cold but nothing that a few nebulizer treatments won't help.
This is the longest either of them has been this sick in such a worrying way. I know it's probably a virus that she'll finally kick in the next couple days, or we'll get a call saying she does have another infection, but it's hard not to let my mind go in worrying directions the longer this goes on with no change.