My allergy symptoms have graduated to violent productive coughing mucus coughed-up ranges from golden/ lime to deeper brown/olive in color. And chest burns w/cough.

There is no way a thousand doctors online could possibly answer this, of course.
We don't even know where you live and what your known allergies are!
The usual process is to try various OTC allergy drugs and see what works, if anything, and to check what pollens are high at the moment where you live.
If a bronchial cough is present after about 3 weeks, see a doctor about possible bacterial infection and an anti-biotic, but beware of taking them too often in your lifetime. You can become resistant, and the bacteria can too, and that's not good for the world.

If you cough is that productive, see your doctor. I thought I had severe allergies because of constant upper respiratory infections and ended up finding out I have a immune system deficiency. GET IT CHECKED