My cough/chest congestion is not going away. I have tried OTC syrups, antibiotics, nasal irrigation. What could be issue. Mornings are the worse.

Depends. I would need more information, i.e., duration of cough, related symptoms (shortness of breath, heartburn), risk factors (smoking, caffeine, eating before lying down), past history (asthma, gerd). It is possible whatever infection you had resolved, but your airway is still inflamed - a trial of inhaled or oral steroids may help. It is also possible that you have GERD. follow up with your clinician.
Allergy. The problem is we are treating life time problem like allergy as a temporary cold,you need to stay on Zyrtec D or Claritin D for two weeks then to the plain one daily. For up to three month or it could be up to a year or a life time. You need to eat a full table spoon of your own local honey daily to three times a day, you need a hot green tea with lemon and honey nightly with Benadryl (diphenhydramine) 25-50mg .
CXR. A chest X-ray may be in order of none has been done. You also need to see your md and get a full exam. I would avoid emperic treatment for now. Often recovery can take a few weeks. Avoiding smoking is key.