Hello, my name is***** and I have over 20 years of experience as a veterinarian. I understand that you are concerned about the amount of sneezing that your kitty has been doing, and a decrease in appetite.
A sneeze simply means that something is irritating his nose. It can be dust, pollens, an irritating, strong smell, increased tearing draining into his nose, a viral, bacterial or fungal infection or a foreign body, a tooth root infection or nasal mass irritating the nasal mucosa.
If this were a one time thing then dust, pollen, a strong smell, or increased tearing would be most likely.
Since this is lingering and his appetite is off I would be more inclined to think of an infection (fungal, bacterial or viral), a foreign body (blade of grass, a grass awn), a tooth root infection, or mass in his nose. Cats that cannot smell their food often eat poorly, so nasal congestion can lead to a poor appetite.
If he has no, or a little clear, nasal discharge, is eating and drinking normally, and his nose conformation is unchanged (no swelling or bumps) then it may be a viral infection, in which case this should pass on its own.
You could try giving him an amino acid supplement called L-lysine at a dose of 500mg orally twice daily. If this infection is due to Herpes this amino acid interferes with virus replication and will shorten the infection's duration and severity. Good supplements to try are made by the Viralys brand which comes in a powder to add to the food or a tasty gel.
In the meantime using a humidifier in the room he sleeps in most of the time, and/or taking him into the bathroom with you when you run a hot bath or shower to breathe in steam/humid air can help. Steam soothes irritated airways, and thins nasal mucous making it easier and more comfortable to breathe.
If this becomes more chronic and he continues to sneeze beyond a couple weeks, and has any sort of change in the conformation of his nose the next step would be sedation, dental radiographs to look for bad tooth roots, a nasal scope and skull radiographs to look for a foreign body or mass. It may be helpful to collect samples for bacterial and fungal cultures as well.
Please let me know if you have any further questions.