1997 Chevy Tahoe battery light in dash.

My battery light in the dash is lit. I noticed that when I hit the brakes while driving, the voltage goes down on the battery gauge. Then after I let go of the brakes, the voltage goes back to normal. Same with the headlights. Is that an alternator problem? Also before this problem began, the truck was screaming like a banshee and would stop after about ten minutes of driving unless it's a cold or wet day (it would scream longer). Once the battery light came on, the screaming stopped. What gives?