If I was standing in front of the car with a voltmeter I could answer your question in about 15 seconds. Car not running, battery voltage should be about 12.2 to 12.6 volts. If its drained it would be lower. Start the car, voltage at the battery terminals should rise because the alternator is charging. You should see 14 to 15 volts. If you see voltage at or lower than you tested with the car off (12.2 to 12.6 volts), the alternator is most likely bad and the car is running off the battery. But is could be a wiring issue, or a starter issue because you didn’t give us any voltage data in the post.
Oh, and stop letting the dimwits at Autozone test your 2 year old car. Its cost you a battery that probably didn’t need replacing only recharging. Let real technicians diagnose the actual issue rather than throwing parts at it.