The white bits are dead white blood cells which have done their job of killing infection.
Questions you should perhaps be asking your GP should include the safety and effectiveness of the procedure.
At one time, this operation was commonplace, but is now being performed less and less, as the evidence suggests that it is somewhat innefective.
True tonsillitis is indeed a pain, and can make you feel pretty rotten, but it is usually self limiting, and patients make a full recovery. Weigh this up against the risks of a surgical procedure, which may not actually help your condition.
Are you looking after your health generally?