Alternator / Battery

Car Wouldnt start this morning (no click no crank) charged up the battery just enough to get it started, drove for maybe 10mins then parked it and it died, jumped it drove another 10mins and died again while in traffic jumped it again drove it to school n gave it a quick charge 20amps for about an hour. It made it to an autozone (20-30min drive) battery was at 12.6 but alternator said it was kicking out I think he said only about 12.4-6v.I jus replaced the alternator a month a ago, the battery lamp is not on, I wanted to know what else the problem could be and how to go about checking it. My battery connections are kinda loose not super loose but movable but that couldnt be the reason why my alternator isnt puttin out enough, could it. Or could it be volt drop in the circuit somewhere? I have a volt meter but I wouldnt know how to go about that if it was a possibilty. Please help