Whole family uses same AppleID - can I block them from receiving my iMessages?
If it is your Apple ID - you should log in and Manage your Apple ID to change the password, remove all emails that are not yours, and update addresses / phone numbers so that only your personal ones are listed.

If the ID is not yours, you will either need to trust that the person controlling the account has done this or open an Apple ID support ticket to ask what the legal department contact information is so that you can justify to an Apple employee why they would modify an existing record to detach any of your personal data from an account you no longer control.

Obviously, your phone number is yours, so you can set up a new Apple ID and register that phone number to correspond to your new Apple ID and that would mean that "your messages" would only go to the "old Apple ID" if people keep sending messages to that email. This only matters if you use an iPhone with iMessage and not an email address.