Your cough could be allergic and thus 1 of the causes for persisting so long even after taking ajax.
Are you also having any weight loss, kiss of appetite?
Take medicine - Allegra-M or Montek-LC 1 tab once a day at night. For 1 week.
Syp. Zeder 2 tea-spoon 3 times a day
Next Steps
blood test - CBC and montoux
Health Tips
warm water gargling 2-3 times a day with a pinch of salt