Thanks for your question on Health Care Magic.
I can understand your concern.
By your history and description possibility of either
lung infection or
bronchitis is more.
In both these conditions, cough with expectoration is seen. And you are not improving with routine cough syrups.
So better to
consult pulmonologist and get done clinical examination of respiratory system, chest
x ray and PFT (Pulmonary Function Test).
Chest x ray is needed to rule out lung infection -
pneumonia.
PFT is needed to rule out bronchitis.
You may need antibiotics, inhaled bronchodilators and inhaled corticosteroid (ICS).
So better to first diagnose yourself and then start appropriate treatment.
Hope I have solved your query.
I will be happy to help you further. Wish you good health. Thanks.