Thank you for your query at AskTheDoctor.com
I understand your concern.
You seem to have a lower respiratory tract infection which has led to bronchitis. It could also be an allergic manifestation where the other symptoms such as runny nose and sneezing will be present.
I will advise you to start taking an anti-tussive like Ascoril Cough syrup twice daily till the cough subsides.
If you have additional symptoms of fever, myalgia e.t.c associated with coughing, you will need to start on antibiotics for lower respiratory tract infection. Cefixime is a good choice and you can start the medicine after discussing with your physician.
If the cough persists beyond 2 weeks, kindly get an x-ray done and follow your physician's advice.
Hope this was helpful,
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