Hi, welcome to HCM. Can understand your concerns.
Cough with phlegm in a 6 year old child can be due to upper
respiratory tract infection like
pharyngitis,
tonsillitis, viral infection of throat.
* viral infection of throat resolves in 3 to 4 days without antibiotics. Cough syrup is usually sufficient.
* in pharyngitis, there is cough with phlegm. There is throat pain and
fever is usually present.
* in tonsillitis, there is throat pain, cough increase at night. Fever is also present.
* Take some precautions like avoid cold drinks, ice-cream and cold water.
* in my opinion, if cough is persisting then antibiotic like cedpodoxime should be given.
* an examination by
ENT specialist should be done so that proper diagnosis and treatment can be started.
I hope this will help you. Wishing your child good health. Take care.