I have had my tonsils remved and have a itchy throat, wet cough, and white spots on the side of my throat in the back. What is this?

Ask an ENT. This may be normal healing if surgery was less than two weeks ago. Thrush is another possibility. Go back to your ent. See also http://www.Richmondent.Com/assets/downloads/ear-nose-throat/throat-mouth/tonsils-adenoids.Pdf.