Story: The protagonist comes from a long line of pharmacists, their family is famous for a certain medicine that only they can produce. The family's dark secret is a genetic disease that occasionally takes the life of a family member causing that person to smell like flowers in the last few days of their life. Once they've passed, the family uses their remains as fertilizer to grow the special plants used to make the exclusive medicine.
The protagonist's school friend notices the floral scent one day, and soon after there is a funeral for the recently deceased protagonist– except they aren't dead yet. The protagonist has gone to wait out their remaining days in at home, they will only die on the first day of spring. The friend (and romantic interest) finds them hiding out, resigned to death, and talks the protagonist into running away together, traveling the world to avoid springtime and death.

For years I have assumed this story was by Sumomo Yumeka and existed in an anthology I owned, but I have just looked through the book I thought it was in, and cannot find it.

This was probably published in english in the late 2000s maybe early 2010s.

Thank you for your help!

You were right about the author, it's Fuyu no Hana, I quickly found it since you already mentioned the author 😛 read it ages ago too