Maybe the alternator pulley, bearing, or something else belt driven starting to seize

Here's what a bad alternator pulley sounds like:

 

You can try using a mechanics stethoscope, long screw driver, a stick of wood, etc. to see if you can find where the sound is the loudest.

You can also check for red-ish brown dust on the face of the alternator around the pulley.

 

Same thing just happened to me. I replaced the alternator.

 

It sounds to me (without hearing it) that you've got either a bad alternator bearing or more likely a squealing belt related to a bad alternator bearing. I'm basing my thought on the battery clue -- it probably isn't getting charged.

 

Hello Everyone! I am not skilled with auto repair, so I had it taken to a shop. They are replacing the alternator and idler pulley!