Is is my battery or alternator?

I have a 1998 honda accord ex 4 cylinder. My starter jus went out and was fixed. Autozone lost my battery i took in to b recharged and replaced it wit a "new battery" they got from the back. I've drove my car fer less than 48 hrs and now my car won't start. I didn't leave any lights on n the night before i had to push down the automated locks by hand. Someone said its my alternator, but i haven't had any problems wit it before. No lights were left on or doors open. Not even my stereo or my headlights were left on. Could it really be my alternator or did Autozone give me a bad battery?

First you have to get the dead battery charged. Then, using a voltmeter, start the car and measure the voltage with the engine running. It should be at least 13.5 volts. Leave the meter connected while you turn on the blower motor, headlights, rear window defogger, and wiper. Increase idle speed to about 2,000 RPM. Voltage should never drop below 13.5 volts. If it does, the alternator is bad. If it passes that test, then you have a parasitic battery drain. Read this post on how to find out what's drawing power when the engine is off

Take it back for a better battery, they lost the original