Vicki --
This one shouldn't be a mystery, it's an easy one. Presuming your idle is set for at least 800-900, measure the voltage across the two battery terminals while the engine is at idle. The voltage should be at least 12 volts. Increasing the rpms a little to maybe 1200-1400 should increase the voltage you read at the battery to full alternator output of about 13.5 volts.
Anything over 12 volts tells you the alternator is charging. Also, anything under 12 volts will turn on the alternator light (dim at first, brighter as voltage drops further below 12 volts).
If your idle is below 800-900, you may not be spinning the alternator fast enough to generate 12+ volts -- thus the red light.
Or (highly suspect) if your fan belt is slipping, then that may cause the alternator not to spin fast enough. Since this is the "noisey" fan belt that is now wrapped around a "new" pulley (and belt tension is adjusted by that new pulley) one wonders if belt slipping might not be your problem.
Anyway, if you get the red light when the engine is running it is probably because:
RPM is too low to spin the alternator fast enough to generate 12+ volts.
The fan belt is slipping, which is causing the alterntator not to spin fast enough to generate 12+ volts.
The alternator doesn't generate 12+ volts because it is defective.
Makes sense?
Mark