Please Save My Earth(1986)

Boku no Chikyuu wo Mamotte

Life's hard when you're shy, harder still when you move from your quiet hometown to the bustle of a big city and a new high school. Poor Alice also has to cope with being regularly harassed by the bratty neighbor boy, Rin. Her life turns upside-down when she's stuck babysitting Rin and the annoying chore ends in unexpected tragedy. What Alice doesn't realize is there could be a greater force at work than unhappy chance!

(Source: Viz Media)