The Realms of the Blood* books by
Anne Bishop.
High Fantasy (i.e. doesn't take place in an Alternate Universe Real World, takes place in a brand new universe) that follows the story of a girl who is born to save the world. Unfortunately, her family thinks she's crazy (because she's friends with various legendary people and beings, including unicorns and magical animals), and commits her to an asylum for "over-excitable" girls. The asylum is a front for a bunch of child molesters... but Janelle really was born to save the world and is more powerful than anyone knows.
The society is based on magic; people with magic are called "the Blood" and people without magic are "Landen". There are also Blood animals, but the people don't know about them. The strength of magic is determined by the color of Jewel that a person can link with; lighter colors are less powerful than darker colors, and women are generally more powerful than men.
Start with the Black Jewels Trilogy; Daughter of the Blood, Heir to the Shadows and Queen of the Darkness. Then read the Invisible Ring and Tangled Webs
*Actually, anything by Anne Bishop is really good, but I think you'll like these the best.