According to Ayurvedic medicine, you have vata induced
cough.
Ayurvedic treatment can be taken along with other medicine since it is a herb based treatment.
Ayurvedic treatment normally starts with body Cleansing as a vitiated body cannot absorb the beneficial effects of medicine.
For cleansing, please take castor oil 1 tsp mixed with 200 ml lukewarm milk before bed.
continue for a week's time.
Treatment
If you have access to Ayurvedic medicine, please take following medicines
Adrak Pak - 5 gm with honey , morning and evening. For best results, ensure no eating 1/2 hour before and after the medicine intake.
Agastya
Haritaki - 5 gm with honey along with Adrak pak
Kanakasava - 50 ml mixed with equal amount of water after lunch.
Lavangadi vati - SOS, suck 5-6 tab to stop cough attack.
Best of luck!