It would have been better if you had mentioned what antibiotic was given and the dosage.
Your symptoms are suggestive of sinus infection
The infected phlegm (mucus) from sinuses
comes via nose to throat causes infection there leading to sore throat
and irritates voice box producing cough.
Persisting infection with toxins in blood causes tiredness
Probably the bacteria were not sensitive to the antibiotic given or the dosage was not adequate.
Generally Co-amoxyclave in adequate doses with nasal decongestants for a week gives good results.
For this you please see an ENT specialist
Wish you good health.