Hello,
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Unilateral tonsillar enlargement may result from infection, chronic inflammatory response, or neoplasm. Neoplasms that commonly produce a unilaterally enlarged tonsil include lymphomas (lymphocytic and histiocytic types) and squamous cell carcinomas. It may or may not produce swollen lymph nodes in initial stage.
The diagnosis can be confirmed after a CT scan and a biopsy of the tonsils. You should go ahead with the CT scan and tonsillectomy as advised by your doctor.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care.