On your phone.......
Tap Settings
Scroll down and tap Messages
Tap Send & Receive
Make sure that the check mark only appears next to your phone number
If there is a check mark next to another number......(your son's).....tap on that number to remove the check mark
Since you are sharing an Apple ID with your son......this may or may not help.
If it does.....you will need to get a hold of your son's phone to perform the same type of check......to make sure that he is not seeing your messages......unless you want him to.