My friend that teaches at the high school level has a student that is constantly informing her of things of a personal nature such as what she did with a boyfriend of sneaking out at night. The teacher has discouraged the behavior but is wondering if she needs to inform administration.
I would also make sure to discuss boundaries with the student when another coworker is present. This sounds like a student seeking attention or possibly just wanting to put the teacher in a bad position. I would definitely tell the counselor, principal and maybe even have a conference with the parents.