Hello and Welcome to ‘Ask A Doctor’ service.
I have reviewed your query and here is my advice.
You have mmentioned that he "coughs up greenish-yellow" phlegm/mucus, than this is cough and probably is caused by acute bacterial bronchitis
or from a bacterial tonsillofaringitis.
Your son needs a physical examination(tonsills and lungs) to decide the diagnosis.
You can continue giving him Tylenol
3 - 4 times a day, as long as he has fever
or pain. He has to rest, drink plenty of flluids.
After the examination the doctor might put him on antibiotics and mucolytics.
Hope I have answered your query.
Let me know if I can assist you further.