Cats can get allergies, but the symptoms are generally itching and overgrooming, not sneezing. If one of my cats started sneezing frequently, I'd have my vet check his nasal passages for polyps or foreign bodies like weed seeds.
I went through a period with Tiger with intermittent sneezing periods and a watery left eye a while ago. He would also shake his head as if he was congested.
It started in May 2010, he had a 3 week period of these symptoms and then nothing for 6 months when it started up again.
I discussed it with the vet.
It was a question of determining whether it might be due to a foreign object or something else. If I remember correctly other possibilities were a virus , I think chlamydia or the worst case scenario a polyp in the nasal cavity.
I did some research into that and the vet said he would have to have an endoscopic exam to investigate the polyp possibility.
I decided to take a wait and see approach as I though the endoscopic exam would be very stressful.
It did occur to me and the vet that it might be a seasonal issue based on the months without symptoms.
In the meantime I decided to look at all other possibilities .
I changed his clay litter to a dust free saw dust (feline fresh)
Although I already kept the house clean I was extra vigilant in terms of regular dusting and vacuuming.
I was already using cruelty free/green household products for the most part but around that time went 100% .
Following this he had no issues until around a month ago- after a year symptom free.
Shortly before this I had used arm and hammer carpet deodorizer powder on his cat tree.
I'm fairly sure this was the reason for Tiger's issues .
The whole time he had the issues I lived in an apartment with carpet and sometimes used the carpet powder.
I then moved into an apartment with hardwood floors and up until the time I used the powder on the cat tree he had been symptom free .
It took me a long time to piece this together and thought I would share .