Worried and confused mommy here Begging for the reply Plss

My 6 year old having a wet cough after getting the cold ,it just started with a mild fever,sore throat and runny nose and after a week the coughing started and having coughing for almost 3 weeks now but it is not persistent but his breathing ok no wheezing and sleeping peacefully eventhoigh i went to kk emergency 2 weeks before they said its just a post viral cough and no need of med but still i haved booked an appointment with respiratory specialist on Tuesday in the meantime i was much worried about my 6 year old coughing? Has anyone experienced bronchitis?is this curable and treatable ? But he inthe referral it is mentioned as he is lethargic as my husband was very worried and told dr that he feels but he is active doing all his homework and playing the coughing wont disturb his lifestyle but 2 times he coughed and spitted light yellow phelgm Pls pls reply mommies