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You could be having this specific problem, a kind of asthma called as ‘cough variant asthma’ or CVA, which may be getting overlooked. The only symptom is chronic cough. Please check in with your doctor and you may discuss this possibility with him/ her.
You can have a look at this resource for more information:
Hope that this helps. Best wishes. Please feel free to enquire if you have any remaining concerns or doubts. It shall be my privilege to help you as much as I possibly can.