I've noticed over that past week or so that the voltage when the car is running is around 11V and sometimes it jumps up to 12.8V and sometimes over 13V.

Does this mean I need a new alternator because of a bad voltage regulator?

Also, the car starts normally (it doesn't crank slow or anything)!

 

sounds low... both my cars have always ran around 14-14.4 consistently. Not sure if that's a sign of a bad alternator, but it definitely seems lower than normal.

 

most autoparts stores can test for a bad alternator.

that voltage sounds fishy, but i wouldn't try fixing something untill you know what's broken... or if it's broken.

find a place that can do a "starting/charging" test. this will give a difinitive answer.