Dry cough needs to be evaluated to rule out allergies. You may need to undergo pulmonary functions test. If all the tests are normal then it may be post viral cough which is a common type of dry cough syndrome after an attack of viral upper respiratory tract infection. Usually it will resolve on its own within few days. You can use dry cough syrups, strepsils like lozenges, steam inhalation for symptomatic relief
Next Steps
Consult nearby ENT specialist for confirmation of diagnosis and appropriate treatment if required