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Cough can last a couple of week in such a case . Fever is usually the first to respond in cases of chest infection. So if your daughter does not have any fever and chest pain and just a dry cough this will also get better . She can take some anti histamine like Cetrizine or Benadryl and mucinex to help ease the symptoms.
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Has she got any fever ?
Which antibiotic was given and for how many days ?
Ok . I think you should give him the medicines I mentioned , In case if she does not feel any better in a couple of days then get a review from your doctor.