The Winter Duke Book by Claire Eliza Bartlett (Author)

All Ekata wants is to stay alive -- and the chance to prove herself as a scholar. Once Ekata's brother is finally named heir to the dukedom of Kylma Above, there will be nothing to keep her at home with her murderous family. Not her books or her experiments, not her family's icy castle atop a frozen lake, not even the tantalizingly close Kylma Below, a mesmerizing underwater kingdom that provides her family with magic. But just as escape is within reach, her parents and twelve siblings fall under a strange sleeping sickness, and no one can find a cure.