Hello

There isn't a way to make sure he is spying on your phone. Logins to your Apple ID aren't recorded. You could change your password.

 Apple ID Password Change

 What to do after you change your Apple ID or password - Apple Support     I suggest doing this before you change your Apple ID or password.

If you are each using your own Apple ID, changing your password won't change iCloud Family Sharing. If you are both using the same Apple ID, it will affect iCloud Family Sharing.