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You can get cough due to many reasons like;as a result of common cold;allergic cough
due to smoke or dust;due to infection of upper and lower respiratory tract;due to irritation and dryness of throat.Since you have had cough since a month you need to consult a doctor in person.Even allergic cough can last for month but as a golden rule it is always advisable for a person to get investigated if he has cough for more than 15 days.Many time it is seen that infective cough like that of tuberculosis;pneumonitis
can be diagnosed at early stage if investigated in time.Since you say that you do not have symptoms of cold or headache and even you have not mentioned about fever
in such a case it seems that your cough may be more likely to be allergic and it requires to be treated.Also see if you have fever or fatigue
in evening;loss of appetite;loss of weight.The best thing to do is to consult a doctor close by get examined and if needed get basic investigations like CBC;ESR;X-ray of chest (if advised by your doctor after he examines you) and then he will treat you accordingly.
Hope this answers your question.In need for more detailed advice please feel free to write me.