This sounds like The White Order one of the Saga of Recluse novels by L.E. Modesitt Jr.
This novel starts the story arc of Cerryl, a young orphan who has the powers of Chaos inside him.
The story follows him working as a mill boy, then an apprentice scrivener in Fairhaven until he is ordered to go to the White Tower, to learn to be a white mage.
The screening occurs early on when he finds a sliver of a mirror and scries a young girl (Leyladin). He meets her in person later in the story.
One of the tasks of the student mages is to learn how to wield chaos effectively by cleaning the sewers of Fairhaven.
The sequel is Colours of Chaos and details Cerryl's rise to High Wizard of the White Order, and his struggles to reform the guild.