My battery only gives off 11.8V when the car is running with all accessories on. With none on it gives 13.1V. Please tell me if my alternator is good.

 

Your alternator is doing something, or you would never get a reading more than 12 volts. I would suggest taking the alternator reading on the clamps, because if your battery posts are corroded you will not get a true reading. Cleaning the battery posts, and making sure connection is tight is always a good place to start troubleshooting. Alternator reading should be at least 14V. Voltage alone cannot troubleshoot alternator problem, but if you are not getting at least 14V it probably has a problem.

 

Sounds like the diods or you resistor, or possibly both, are fried. I had the same issue with mine a while back. Do you have an upgraded sound system in your car?