What Causes Persistent Cough With Thick Sputum While Having Dysphagia?

I was just diagnosed with neurogenic cough. It has persisted now for about six months. I am allergic to grass, trees, dust, smoke, etc. I also have acid reflux. I chronically clear my throat, but rarely cough anythig up. But when I do, it is thick yellow green phlegm. I constantly feel as though I may aspirate the pooled mucus. I have titanium rods and a 2x4 inch anterior plate in my cervical spine. I also have dysphagia. My condition is constant and cannot get over it. Please help.