Messages on two devices

I just have a theory as to what's going on, but I could use some help. I typically only text from an iPad with this Apple ID. However, I recently logged into messages with that Apple ID on a Mac. A couple days later, during which I didn't text from the iPad, I tried to send a text from it and I got a send message failure alert. I honestly just assumed the person had blocked me on accident, but she didn't. I tried texting several people with same results. My wi-fi's fine, I have excellent connection, and I'm still getting emails and notifications from other apps. I figured it would be the same from the Mac, but I checked and realized I'd received several texts which came through on the computer but not the tablet. Also, I can send texts from the computer with no problem. I thought maybe if I logged out of my Apple ID from messages on the computer, but it seems there's no way to do that without logging out from everything on the computer. Any help?

Thanks!

Banter