Ame ni Utau Ballade ~A Rainbow After the Rain~

Throughout the game you are presented with various flashbacks of a psychiatrist talking with a girl named Ame.

At the start of the story the protagonist lives with Chinatsu due to various happenings in his childhood that caused him to become an orphan, and as such mainly sees her as an older sister. The prologue basically starts out with Chinatsu telling the protagonist that 3 of her patients will come live with them for a few weeks as a part of their rehabilitation.

[From xelivous review]