Hello, my name is***** and I have over 20 years of experience as a veterinarian. I understand that you are concerned about William's sneezing/nasal congestion with some bloody mucous despite being placed on an antiviral drug and I'd like to help.
It would be nice to know if the discharge from both sides of the nose, but I can understand that can be difficult to figure out if the sneeze sprays blood across his nose.
Sneezing and reverse sneezing are signs of nasal and pharyngeal irritation.
With nasal irritation we can also see a nasal discharge which can be yellow, white, green, mucoid or even bloody in character. In some cases with long term infections or a mass we can even see bleeding and nasal bone destruction and swelling or changes in nose conformation or around the eye.
Possible reasons for these symptoms are bacterial, fungal, or viral infections, a foreign body in the nose, a polyp or mass in the nose or a tooth root infection. Another possibility is a sterile inflammatory condition called lymphoplasmacytic rhinitis.
Lymphoplasmacytic rhinitis is a chronic inflammation and thickening of the nasal mucosa that does not cause any changes in the nasal bones, and is not associated with any sort of infection. It is steroid responsive, but high doses of steroids for long periods of time can be rough on his gastrointestinal tract, liver and kidneys and can cause diabetes. Ideally we get the condition under control with a high dose of steroids and then slowly reduce the dose to the lowest possible to control the condition. Some cats can come off steroids completely for long periods of time without symptoms returning, but most need steroids chronically at lower levels.
Because we need to use immunosuppressive with this disease we want to make sure we look for infectious causes first and rule them out, and get biopsies for a definitive diagnosis.
Allergies are rarely the cause of chronic nasal congestion, cats seem to get itchy with allergies, not nasal congestion.
Diagnosis of a the problem behind these symptoms can be complicated. We may need to perform radiographs of the nose and sinuses looking for changes in the bones or full sinuses, nasal flushes and scoping to collect culture and biopsy specimens and sometimes blood titers to look for the infection (especially if we are suspicious of a fungal infection).
Ideally because he has pica too we would run some blood tests including a complete blood count, biochemistry profile and feline leukemia and feline immunodeficiency tests. Some cats exhibit pica (eating or licking/biting non-food items) when they are anemic or sick and we do want to make sure that he is healthy and there is not a physical reason for his behavior. After having nose bleeds for a while he could be anemic. Or suffering from metabolic organ disease that interferes with clotting, or an immunosuppressive virus such as feline leukemia. This can also be a sign of nausea. To check general health I would start with a complete blood count and biochemistry profile and T-4 as well as testing for feline leukemia and feline immunodeficiency viruses.
If those tests come back normal then looking for a tooth root infection, a foreign body or polyp with a nasal scope and radiographs of his tooth roots, nose and sinuses under sedation would be recommended. A biopsy of any abnormal tissue could be diagnostic.
I would also check for a fungal infection by checking blood titers for fungal infections found in your area, aspergillosis tends to cause nasal congestion and infections throughout the US.
If you decide that you cannot or would not run any further diagnostics, and his physical examination is relatively normal then trying an antibiotic such as Clindamycin, Doxycycine or Clavamox could be an option. These antibiotics are good for treating tooth and respiratory tract infections. But unless the infected tooth is found and removed then the problem is likely to return. So this is by no means a long term solution.
Best of luck with your fellow, please let me know if you have any further questions.