The tentative diagnosis is a sinus infection. (I didn't know cats could get sinus infections.) I've got tuna-flavored liquid antibiotic to give her every day for a week, and the vet's email to send updates or questions to. She (good vet) had me make a follow-up appointment for next Wednesday, but depending on how things progress, I might not need it. Or might need to go in sooner, if this doesn't seem to work. Vet also noted that on Agatha's last blood work her blood sugar was a little high, so we need to watch for diabetes.
Current status: Agatha is in her usual evening spot here on the desk, under the heat of the lamp. There's a lot of snorting, swallowing, and the occasional gakking fit going on, and I wish I could hold up a tissue like parents do to toddlers and say "Blow your nose, Agatha! Harder!" Unfortunately this doesn't work well with cats. :(