I just opened Messages>Preferences>clicked on my Message account, clicked the minus sign. It prompted me to login to my AppleId. I entered it and it worked, though I had to quit and restart messages. Basically just needed to login to my Messages app again because I'd changed the password--I thought it was my having downloaded the latest version of Mac OS, but I guess not.
MacBook, OS X El Capitan (10.11.6), null