I do not know the author or the name of the book but it was published about 1947or 1948 It was the same time I read Elizabeth Enright's "Four Story Mistake."

It was about a girl who had very little in common with the kids in her school and had few friends and believes it will be worse now that she has moved. She is standing on a bridge in the new town and down at a field when a boy joins her and says "white sheep in a green field, doesn't that remind you of "Kim". That was just what she was thinking and she makes her first of many friends in a school that shares her interests.