Tonsils are ovoid-shaped immune glands located at the back of your throat (there is a right and a left tonsil). When your tonsils are infected, you will experience severe sore throat, painful swallowing and fever. If you look at the back of your throat in the mirror, you may see white patches or pus on the tonsils itself.
Treatment of tonsillitis (tonsil infection) typically involves a course of oral antibiotics, pain relievers, gargles and lozenges. Majority of bacterisl tonsillitis resolved within 10-14 days after starting oral antibiotics.
As your symptoms have been persistent and lasted longer than the usual episode of tonsillitis despite being on antibiotics, I would suggest a reassessment by your General Practitioner or by an ENT Specialist to exclude other causes of sore throat.
Hope this helps and all the best!