1) Actually latent herpes is a strong possibility.. think of it like shingles in people. The herpes virus is introduced early in life with or without symptoms and lays latent until the animal ages and immunity wanes.
The number one cause of sneezing and sinusitis in cats is herpes. The virus invades the mucous membranes and can cause chronic erosive lesions in the sinuses.
If this is latent herpes, lysine orally and hyper-immunizing with intranasal FVR vaccine are most helpful. Antibiotics are only helpful as adjunctive therapy for the inevitable secondary bacterial infection. Herpes tends to be chronic (like shingles) and waxes and wanes in symptoms. However, once sinusitis sets up, it is rarely cured and difficult to control.
2) Another cause of sneezing and runny noses in cats is chlamydia -- antibiotics is the treatment of choice. Clavamox is ok, doxicycline is better.
3) Allergies. If this is allergies, then it should respond quickly to cortisone. This would be a diagnosis based on clinical response. A single dose of depomedrol given IM would make a huge difference if this is allergy. If on the other hand, it is herpes, steroids would probably not help and may reduce resistance further -- so close observations would be important. A single steroid injection would not be dangerous for the herpes, but if it didn't give dramatic results, I would lean towards thinking this is herpes.
I hope I have helped and answered your question. I am willing to work at clarifying something if I need to.