yes, sounds like an altenator, but....
if your battery is really gone bad it can take down the voltage also.
take the battery out of the car and try charge the battery with a charger, after a few hours stop charging, measure the voltage and after an hour again.
if the voltage drops ( not by a tenth but whole voltages) then the battery is really bad and probably not the altenator.
you can also take a battery from your neighbour
and put that in your car and measure the voltage then if the car runs, if its low again like you said, the your altenator is gone bad. if its about 14-14,5volts its ok
sorry for my bad english but i hope you got some answers