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First you should do its to get a NEW MICRO sim card, second, which version do you have? C6806 or C6833?
3G Network
850 / 900 / 1700 / 1900 / 2100 - all versions Thi should work with either T-mobile or AT&T's 3G
4G Network LTE
700 / 850 / 900/ 1700 / 1900 / 2100 / 2600 - C6806 This should work with AT&T's LTE 4G
800 / 850 / 900 / 1700 / 1800 / 1900 / 2100 / 2600 - C6833
a MINI SIM card it is NOT the same as a MICRO SIM card, you might damage your phone if you force it in your Xperia Z Ultra
I'm in the USA too, how old is the micro SIM card? it doesn't recognize the SIM card at all or it doesn't recognize the network?