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After reading your complaints regarding throat problem, and analysing the symptoms and after co-relating these with possible pathological process it appears as you are having chronic tonsillitis
. The white particle which you get are being discharged from your tonsils and these are formed by organised pus in follicles of tonsils.
Once tonsils starts giving out these type of paticles than usually conservative treatment fails to cure it and operation of tonsils becomes the choice of treatment.
You may consult your ENT doctor for examination and necessary investigations for plan of treatment. If your doctor too sugest for operation than do follow that as to avoid complications.