1) Did you believe the story I told you? (correct)
2) Did you believe the story I told you about? (incorrect though possibly usable in some contexts)
3) Fran is the aunt I told you. (incorrect)
4) Fran is the aunt I told you about. (correct)
"Told about" describes something (the story) to the person you are talking to.
Told means you actually told them the story ie they have experienced it.
You can not "tell" somebody a physical object (like an aunt) because tell implies the transferal of information via speech (you can tell people stories, information, etc) .
Tell about is ok because you are describing the aunt ie passing on information.
Student or Learner