The Thirteenth Child by Erin A. Craig

All gifts come with a price.

Hazel Trépas has always known she wasn’t like the rest of her siblings. A thirteenth child, promised away to one of the gods, she spends her childhood waiting for her godfather—Merrick, the Dreaded End—to arrive.
When he does, he lays out exactly how he’s planned Hazel’s future. She will become a great healer, known throughout the kingdom for her precision and skill. To aid her endeavors, Merrick blesses Hazel with a gift, the ability to instantly deduce the exact cure needed to treat the sick.
But all gifts come with a price. Hazel can see when Death has claimed a patient—when all hope is gone—and is tasked to end their suffering, permanently. Haunted by the ghosts of those she’s killed, Hazel longs to run. But destiny brings her to the royal court, where she meets Leo, a rakish prince with a disdain for everything and everyone. And it’s where Hazel faces her biggest dilemma yet—to save the life of a king marked to die. Hazel knows what she is meant to do and knows what her heart is urging her toward, but what will happen if she goes against the will of Death?