This is by Riyoko Ikeda, released 1971. The version I read was a 2017 digital republication. It's a single short volume.
Early on it can feel like a silly comedy about a toxic rivalry, but it gets increasingly grim and becomes a tragedy. I think it's possible for a manga to pull that off, but the execution in this story feels immature. A lot of its elements would get remixed and expanded upon in Onii-sama e... a few years later, with the comedy largely excised and the handling of the drama much improved.
The main characters are Kaoru and Reiko, classmates at a posh all girls middle school who frequently clash. They become sisters when Kaoru's working class mother marries Reiko's wealthy father, which makes things even more fraught between them. Moments when they manage to be nice to each other are preludes to another unpleasant falling out. Both girls carry a lot of insecurity and they torment each other for most of the story.
Kaoru does grow to love Reiko as an annoying sister she has complex feelings of guilt and inferiority toward, and Reiko grows to love Kaoru as an irresistibly sexy person she is possessive about, but ultimately the circumstances of Kaoru's parentage and health problems for Reiko lead to the tragic ending.