Wow now, I had a similar problem when I installed a new battery. To my knowledge if the red battery light on the dash is On then it is Not you alternator! Because my truck was dead for about a week the computer reset itself and it couldn't compensate for all of the dust and dirt inside the throttle body. My battery light was on and according to computer diagnostics the alternated wasn't carrying the charge. I found it quit odd myself but Once I cleaned the throttle body fired right up and everything was back to normal. Highly recommend you do that first.