My alternator light comes on when I accelerate

It's a good possibility that the belt is slipping during acceleration, when you check the voltages the engine is probably at idle and there is very little strain on the drive belt. Check the belt condition (glazing, cracks, etc.) also check the pulleys for excessive wear and of course the belt has to be properly tensioned. Good luck with it!!

Check all your ground wires in engine compartment.Wires tend to rust even they look Ok from outside.

I found out the issue was just a loose wire. Thanks for all the suggestions.

It was something to do with wires...I am glad you found loose connection