Manga

A series of oneshots. In one of them a girl is almost hit by a car, but a woman saves her, dying in the process. She tries doing her best to be like that woman help others after that, which one of her classmates finds annoying. He has a little brother, and she befriends the two. She finds out his dead mother is the woman who saved her. The guy finds out when his dad recognizes her, and she runs. The dad tells the guy about how she had written many letters to them. I think there was another chapter where she gets stuck in a tree when trying to help some kids, and he tells her to stop interfering like that.