The voltages you are getting are symptomatic of a bad alternator, not a bad battery. However, disconnect the battery to test. If you read 10.5V or higher, you do not have a shorted cell. Note that 11.9V is what you would get with a discharged GOOD battery, and under charge this should read above 14V when above idle, until fully charged, from a good alternator. A battery that is sulfated and worn out would indicate an overly high charge voltage when charging from a good alternator.

Steve

__________________
'91 MB 190E 2.3
'08 RAV4 Ltd 3.5
'83 Lazy Daze m'home 5.7