14 V is low for a normal alternator. Check if the belt

is too loose for alternator please. Normal voltage should be 14.4 V and above. Maybe that is why your battery is 12.3 V to start with. You could go to a car parts store, Advance Autoparts, Auto Zone, O'Reilley etc, they will check your alternator free. Or you could buy a battery/alternator tester for around $20-30 to check yourself.