A Persistent Hard, Straining Cough Producing Slimy, Clear Mucus. 2

A persistent hard, straining cough producing slimy, clear mucus. 2 courses of antibiotics and prednisone finally cleared this, but now it's back after 2 weeks. Earlier bouts has blood and loss of vocal chords from intense coughing. There is rattling and wheezing in my chest & back. A GP was consulted due to no change in condition despite first round of antibiotics.
I am a non-smoker, & do not drink alcohol.
In the mornings there is green / brown clumpy mucus after awakening, and it loosens with steam from the shower. A chest x-ray is normal. Allergy test shows many allergens, but nothing seems to be in great bloom here at the moment. My nose smells bad on exhale, and sinus rinses have not cleared this.