My asthmatic and allergic little tabby was sneezing a lot and showing signs
that her nose was sore (e.g. snarling and stiffening if we went anywhere
near it while petting her.)

Just an FYI: the vet told me to give her Chlortrimeton (that is the brand
name, there are generics available) at the rate of 2 mgs every 12 hours.
(NOT the kind that also has decongestant, just the kind for allergies.) I
gave her half that (2 mgs every 24 hours) for two days and she has not
sneezed at all today and has been rubbing her face on us as she usually
does. Her cold (or whatever it was) lasted about 12 days, and mostly she was
just sneezing a lot and not quite eating as much as she should. She weighs 7
1/4 lbs, so that dosage is for a cat her size.