Whoooo, get ready to break out the foil hats and the fire retardant suits
AT&T typically stores text messages for as long as it takes to get them delivered and out of the network. That can be up to 72 hours.
Are they monitoring your text messages? That depends. If a law enforcement agency has presented them with a warrant (or sometimes, not even that much) because you're some kind of person of interest to them, then no doubt, AT&T is storing your messages for longer, and monitoring them.
Otherwise, realistically, it's not worth AT&T's time and storage space to keep it all beyond what is necessary to get the message to its destination.
What AT&T does keep track of by default is what numbers you are sending SMSes to and receiving them from, as well as timestamp for each. These will show up on your bill. But the actual content of those messages will not.