Apparently, changing my Apple Password on my iPhone a day earlier messed up the Message app on my iPhone. There was no option to re-sign back in, only to click on the “Forgot password” link. This was not a solution or was it? After my research and trial and error, I gave it a show. I had to create a new password, and when I did, all my Message Settings came back and it re-registered my iPad to send and receive iMessages (And “other” messages too).