My Name is Monster by Katie Hale

After the Sickness has killed off her parents, and the bombs have fallen on the last safe cities, Monster emerges from the Arctic vault which has kept her alive. When she washes up on the coast of Scotland, everyone she knows is dead, and she believes she is alone in an empty world. Slowly, piece by piece, she begins to rebuild a life.

Until, one day, she finds a girl: another survivor, feral, and ready to be taught all that Monster knows. But as the lonely days pass, the lessons the girl learns are not always the ones Monster means to teach.