Can you explain what are these white spots on my tonsils?

Probably tonsilliths: While you can get an exudate on your tonsils when there is an infection, more likely what you have are tonsilliths, or tonsil stones. There are the excretory product of the tonsils that form in the crypts ("pockets"). There are more common in younger people, and often will occur more after an inflammatory process, like a cold or upper respiratory infection.