I can't remember what the movie was, but it was a young girl who has a little baby brother and later reveals it's her son and that they moved so no one would tease her about how she was pregnant so young?
There's an oldie called Susan Slade (1961). The plot revolves around a naive 17-year old girl, Susan Slade (Connie Stevens) who becomes pregnant during a shipboard romance with Conn White, a mountain climber (Grant Williams). Her parents decide that it is best for Susan to allow them to pass the baby boy off as theirs to protect her reputation. Feeling helpless, Susan reluctantly agrees to pretend to be the baby's older sister.