I have a 16 year old Tortie, Mollie Rose, who does that. It was so frustrating. Like running after a sneezing with a tissue to wipe her nose. I took her to the vet and she was diagnosed with kitty allergies. He took xrays of her sinuses to see of there were polyps and there were none. He put her on a dose of Prednisone and Clavamox which helped for a long time. But she's doing it again, and I'm just attributing it to the nice weather we've had these past few days.

Before the vet, I was giving her Chlortrimeton once a day to help with the sneezing, watery eyes, runny nose. It worked great. I'd also use "Little Noses" Saline Drops to help clear her stuffy nose. You can get that at any drugstore. Make sure it is SALINE and not the medicated stuff.

Hope your kitty feels better soon.