Are there any trouble codes setting? The PCM controls the alternator output. From there, have you actually measured the battery voltage before you start the car, then after it's running with everything turned off, running with as many accesories turn on as you can (except for the wipers because you want a steady load). The speed the car up to about 2000 rpm and repeat the measurements. Write them all down and we can then tell you if the alternator is actually charging or not, but we won't quite be ready to tell you if it's bad or not.
That could take more specific testing depending on the results above.