Sorry, had this happen to me - just saw your thread. I suspect it's a race condition when you have some Mac's running Sierra and some running High Sierra with the same iCloud account - it can mess up the credentials.
Presuming you have 2FA enabled (everyone should) - go to the appleID page:
https://appleid.apple.com/
You're going to need to sign all (well, all but one initially) out of iCloud and remove them from your list of devices on the appleID page. You leave the one authorized / signed in, so it can authorize your 2FA. Once you've cycled through all but one, then do the same with that last device.
Note: iCloud may make you change your AppleID password (yes, I know, onerous) - it did with me (so it obviously knew something was out of sync).
Now that you fixed your iCloud credentials, just make sure that all of your iMessage setups are using your AppleID as well as your cell number (with your cell selected as start new conversations from).