Hello, my name is***** and I have over 20 years of experience as a veterinarian. I understand that you are concerned about Buddy's sneezing a great deal and nasal discharge that did not improve with antibiotic and Benadryl (diphenhydramine) therapy.
Dogs very rarely have allergies that cause a nasal discharge. Usually dogs with allergies get itchy skin, so I'm not too surprised Benadryl had no effect.
Possible reasons for these symptoms include a bacterial, fungal, tick borne or viral infection, a foreign body in the nose, a polyp or mass in the nose or a tooth root infection.
Is the discharge coming out equally from both sides of the nose?
Since he is a bit of an older fellow a mass, tooth root infections or a bacterial or fungal infection secondary to a weakened immune system are all more probable causes.
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 nasal bone destruction and swelling or changes in nose conformation or around the eye.
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).
You can do the diagnostics in a stepwise fashion if finances are limited.
Things that you can do that aren't too expensive include checking a complete blood count and biochemistry profile as well as a thyroid panel to assess general health.
Getting a sample of his discharge and looking at it under the microscope for signs of fungal spores would be worthwhile. If we see fungals spores then blood titers and/or submitting samples to the lab for growth would be recommended.
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. Flushing his sinuses and nose under sedation to collect samples for fungal and bacterial infections would be recommended as well.
I understand that an antibiotic was tried but you don't say which one. If you decide that you cannot or would not run any further diagnostics, his color remains good and his physical examination is relatively normal then trying an antibiotic such as Clindamycin or Clavamox could be an option. These antibiotics are good for treating tooth and respiratory tract infections.
Doxycycline could be given instead as Doxycycline is good for respiratory tract infections as well.
Ideally however rather than continuing to waste money "trying things" your fellow would have some diagnostic testing done to find the root cause of his symptoms.
Best of luck with Denver, please let me know if you have any further questions.