Looking For The Villainess's Contract Husband

One day, while suffering from a burning fever, I realized I had been reincarnated as the daughter of the villainess in a novel.
Thanks to remembering the original story, I now knew the future—but it wasn't exactly filled with hope.
My villainess mother is destined to be used until the very end and die, and I, too, am fated to die from an incurable disease.
Still, there was exactly one good thing about this. While there is no way for me to survive, I can at least save my poor mother.
'Live, Mom. In my place, happily.'
To save my mother, I sought out the Duke, who was a minor supporting character in the original story.
"So, please propose to my mother, Your Grace."
Armed with my knowledge of the original plot, I struck a deal with him. In return, the Duke rescued my mother and me from the clutches of my cruel maternal grandfather.
My plan was to slip away and die quietly in a place where no one could find me once the contract was safely fulfilled, but...
"Libby, I think I'm feeling a bit sick. Could you hold my hand?"
Out of nowhere, some sickly, beautiful boy is clinging to me? By the way... is this guy actually sick? Something is definitely suspicious.