I just noticed this post on the iPhone 6s forum:
http://forums.imore.com/iphone-6s/36...ml#post2803366
How did you get the carrier update on iOS 10? I upgraded to the beta but couldn't send SMS messages; Apple help told me it was because AT&T's carrier settings don't support iOS 10 yet (or something), so I had to go back to 9. Any suggestions? I noticed they just did one last beta update but I can't find anywhere that tells me if AT&T will support it yet or if I have to wait five whole days until Wednesday.
So maybe that's the issue? (I'm on Verizon myself, and messages has been working fine on my phone since I installed the beta a few weeks ago.)