Towa Kamoshirenai

From Esthétique:

Kosumo has a serious medical condition that has kept her in the hospital ever since she was a child. Since Kosumo's blood type is rare, it impossible to find a donor.
While Kosumo is on the verge of death, out in the city, the 99th Generation Miko, Himiko-sama, gets into a terrible accident while trying to save a child. She is rushed to the hospital, and there her fate crosses with Kosumo's.
When the hospital discovers that Himiko has the same rare blood type as Kosumo, they decide to make her a donor, since Himiko is sure to die as a result of the accident. Kosumo recovers and moves back to Tokyo, but later finds out that Himiko's blood isn't the only thing flowing inside her…