Severe hoarseness in motor neuron disease patient after surgery for mandibular fixation

I am a 58 year old male who has been suffering from profuse phlegm in my throat for 5 or 6 years, which has made me increasingly hoarse recently and hacking almost all day long. I also have hay fever in the spring, and RAST testing has shown me to be sensitive to many inhalants, including pollens and house dust. In the past year I have used fexofenadine, a second generation antihistamine, and also a corticosteroid nasal spray with fluticasone furoate, but neither of these has provided any substantial relief. In the past I was given injections for desensitization, but these didn't help either.  Besides these, no other treatment has been suggested.

I also have a deviated nasal septum, but until now surgery has not been suggested.

In addition, I have been diagnosed in the last year with a motor neuron disease characterized until now by mild distal muscle atrophy and weakness, slight swallowing difficulties and profuse saliva. The neurologists I have been to say that my disease is mild and probably not the classical ALS.

3 weeks ago I fell on my face and fractured my jaw in 2 places. I underwent surgery for mandibular fixation and now I have braces and guiding bands on my teeth for straightening of my jaw. The phlegm in my throat has increased since the surgery, and I now have severe dysphonia, so much that I can often hardly speak above a whisper.

The ENT doctor at the hospital held that the secretions are saliva from my mouth which I do not swallow due to atrophy of the swallowing muscles and which goes down into my airways. But the phlegm feels much thicker than saliva and is harder to swallow, so I think it comes from my nose.

Finally, I have no clinical symptoms of GERD, even though I have tested positively for helicobacter, like most of the population.

My questions are as follows:

Are there other tests that can be performed in order to determine the physiological cause of my phlegm?

Should I try desensitization treatments for my allergies again?

Are there any other treatments worth trying?

Thank you very much for any comments or suggestions.