I had this issue when I first got my iPhone as well. I think the problem arose from the fact that I ported over my Verizon number as opposed to just getting a new number. As other people have mentioned, my solution was to call AT&T and wait 24-72 hours. (Truth be told it took a couple of calls)
I don't know if this necessarily had anything to do with taking my Verizon number with me, but it is all that I could think of.
In any case, call AT&T and give it a little time and patience; you'll be getting texts again without issue before too long.
I don't know if this necessarily had anything to do with taking my Verizon number with me, but it is all that I could think of.
In any case, call AT&T and give it a little time and patience; you'll be getting texts again without issue before too long.