You might need some other antibiotic like levofloxacin
in addition you may require decongestants both oral and nasal. and antihistaminics.
Ear nose and throat are all related because of the same kind of mucosa ie skin.
So all need to be covered at once and problem at one organ leads to problem at other.
The throat infection
must be causing irritation and so the cough
Get an ENT consultation done and get yourself examined.