Use (and join) AW, or americanwhitewater.org, to check their river resources. There's also info on alabamawhitewater.com (if I remember the link properly).
Alabama whitewater is more rainfall dependent than that in Georgia or North Carolina. The only dam-controlled whitewater that comes to mind is on the Coosa in central Alabama. (No Ocoee or Nantahala with predictable water.) You will need to learn how to follow water levels on the AW site or on the USGS page.