I think what you're remembering is "The View from the Mirror" quartet by Ian Irvine:
- A Shadow on the Glass
- The Tower on the Rift
- Dark is the Moon
- The Way Between the Worlds
This fantasy novel has the sort of world one would find in The Lord of the Rings, as far as it being archaic, yet containing sorcery of some sort.
That fits so far, although as the series goes on, the magic comes more and more to the fore.
The book starts with a young man who has graduated from his school (unclear if it's a college or what, but he has dormed there). Everyone has a job they are meant for. I think he's a teller of histories or creator maps.
Llian is a Chronicler of the Great Tales. As the story starts, he's graduating from the College of the Histories of Chanthed.
He breaks into a section of the library he's not meant to. He flees and runs into a young woman on a quest.
He breaks into the forbidden books section. He gets caught, flees and ends up with Karan, a young woman, as you say, on a quest.
They're captured at some point.
They get captured a lot.
Something with objects and a prophecy. Maybe the young man is part of two species which were thought extinct but are stuck in a parallel plane.
This isn't quite right. The overall plot involves four species, one of which was thought extinct but is stuck in a parallel plane. But Llian was very much human.