I understand that you are concerned about the amount of sneezing that Julius has been continuing to do despite the use of antibiotics.
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.
Cats very rarely have allergies that cause a nasal irritation and sneezing. Usually cats with allergies get itchy skin, so I would not think this is related to allergies.
If this were a one time thing then dust, pollen, a strong smell, or increased tearing would be most likely. Since this is a more chronic thing 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, a nasopharyngeal polyp, or mass in his nose.
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, which in most cases should pass on its own after a couple weeks. Rarely we can see chronic infections that lead to nasal congestion and sneezing.
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. That will soothe irritated airways and thin the mucous making it easier for him to breathe.
If he continues to sneeze 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.
There is also a chronic inflammatory process (Lymphocytic-plasmacytic rhinitis) we see in some kitties that responds well to steroid therapy. It is not as common as the other things I listed, and we would need to rule out infectious agents before prescribing high doses of steroids because suppressing the immune system of a cat with an infectious disease could be dangerous.
Please let me know if you have any further questions.