I just replaced the alternator and battery on my 99 silverado. Battery is showing
about 13 volts and when running showing about 14.8 volts. Looks good but the
battery light is on, on the message center and wont shut off even though everything
is running fine.

 

Along with the red fusable link going from the alternator to the battery there is a connector with i think 4 small wires on it that connects to alternator as well, if you missed the small connector the comp wouldent know the alt was charging.
If thats not the case disconnect the battery cable for a minute and them re connect this might put computer back in learn mode and it might pick up that the alt is charging. [mind you turn your radio alarm off before disconnecting battery].
The fusable link must be ok if it is showing the 14 volts on the battery terminals.