So I had the same problem with two phones - data was working, but not calls (though texts also worked). I don't believe its actually AT&T that is the problem, but that sometimes when your phone first registers on a network it fails somehow, leaving it messed up. What you need to do is register with any other network, then turn back on automatic registration, and let it do its thing.
Phone 1 - was registered with AT&T via automatic registering. Changed it to Verizon and it worked. Changed it back to AT&T and it still worked.
Phone 2 - an additional wrinkle - for some reason - VoLTE calls - Use 4g whenever possible for calls - was turned off. I had to enable this, and also do the force a change of network thing.
One more thing - when I arrived in the USA the phones got a message about some ridiculous addon that would cost over £7 a day and have only 1gb data. Before leaving I had asked them to set up the "Roam Anywhere", which costs £10 a month and extends your whole plan to the USA and Canada. So I was surprised to get the wrong text messages. Upshot was I was on the £10 option, and I checked by testing ROAMING to 150, which confirmed it.
If you are traveling to the USA, or indeed most countries, you should ask about Roam Anywhere, if its available on your plan!
