diagnosis: I think its a stuck key in your keychain for iMessage. all you need to do is to remove it and get iMessage to download the key for your apple id again, but it turns out you can’t without a fiddly process – you have to reset iMessage, and the keys, and trying to log in with a second email address thats associated with your apple id then it should work.
the very first thing you should do is to make sure you have two email addresses associated with your apple id – go to appleid.apple.com > manage apple id > add a new email address > verify it.
then you can start this process:
applications > utilities > keychain access
search for ‘imessage’ select them and delete them
search for ‘facetime’ select them and delete them
you should see a ‘temporary iMessage key’ for your apple id that you can’t delete (yet)
alt+click on go
navigate to preferences
search preferences folder for ‘imessage’ – delete all results
search preferences folder for ‘facetime’ – delete all results
the above steps 5 to 7 turn the ‘temporary key’ in your keychain to a permanent one (albeit with the wrong info in it) that you can delete