A lonely girl named Nanami loses her only companionship, her beloved cat. To try and move on from this terrible phase in her life, she tries to go to a resort to relax, but its not working at all, with the pain of loss still very much alive inside of her. Until, she meets a woman that greatly reminds her of what she once lost...

From DrCoke at MangaHelpers:

Even after one month of transferring to a new school, Natsuki keeps her distance from her classmates. Her childhood friend Haruka always tries to push her to be more sociable, but Natsuki just pushes her away. One day, while Natsuki was skipping class and eating lunch on the school balcony, a slime-like substance drops right on top of her. The slime slowly forms itself into... a human girl? An odd relationship between Natsuki and her new alien(?) sister Aoi begins.