Hi,
   I understand your concern.
    Your 
cough seems to be allergic in origin, secondarily infected by bacterias.
  -  To get rid of the cough I feel the extent of infection,/ bacterial sensitivity to antibiotics should be known (   physical examination by a physician, Blood counts- TLC/ DLC, Xray chest, 
sputum culture & sensitivity test ) & then a full course of antibiotic so as to remove bacterial infection( indicated by excessive cough/
yellow sputum)/ Tab. 
Diethylcarbamazine ( according to blood cahnges0 cough syrup , 
Montek lc  should be given for sufficient days.
  - Allergens recognized & avoided/ desensatized.for prevention in future.
   - avoid cold/ sour things/  exposure to allergens
   - hot saline gargles / vapor inhalaton.
   - drinking warm water 
  With proper diagnosis/ sufficient  treatment/ self care the cough can be got rid of.
   Thanks.