Hello maggies_mom,
Thanks for using Apple Support Communities. We understand that your playlists are showing up on your sons device, and you want to know how to have different playlists. It sounds like you may be sharing your Apple ID with your son. If so, you really want to be sure both of you have your own Apple ID. This way your data is separate, and you can still use Family Sharing. More information can be found in the following guides:
Use your own Apple ID for Family Sharing
Family Sharing and Apple ID for your child
Just in case, we thought you might also find the following guide helpful: Use parental controls on your child's iPhone, iPad, and iPod touch
Thanks again, and take care.