I'm happy that you have asked me to assist you with your child and hope that you can benefit from my many years of helping parents like you.
There are a few possibilities for conditions that could cause him to produce phlegm. First, if he had an infection then then antibiotic may not have completely cleared it, especially if he had a sinus or bronchial infection, as they can take at least 14 days of antibiotics to treat.
Also, if he has fever with this then infection is the most likely cause as other conditions that cause mucous do not cause fever. He may have allergies or asthma, both of which cause excessive production of mucous from the sinuses and small airways in the lungs but not fever.
I suggest that the next time he has fever with mucous/phlegm he be seen by his doctor as he must have an infection that has not be addressed adequately.
I see you are still offline and since chat does not allow me to stay online if you and I are both not posting replies I'll switch us to the Q&A mode since it has no time restrictions. I'll be notified when you return and am happy to work with you.