The battery light usually indicates a bad charging system. My guess is that you are correct, and that your alternator is going bad (or is bad already). You can have Autozone or similar shops check it for free usually.

'97 Extra Cab 3.4 4x4 5sp 90K mi and counting.
Mods: KYB GAJs, Monroe damper, Marlin shifter seats, Kenwood sound, bedliner, Leonard shell, ES sway bar upgrades, Aisin Hubs...Best truck ever
Currently listening to: Ryan Adams and the Cardinals III/IV
Currently fishing for: reds and trout