Car is bucking and my lights are dim

Hey guys, 86 5.0 here. Car is running like crap "power of a 4cyl" and dies a lot when i come to a stop with the clutch in "but starts just fine with no problem". At night the lights dim like crazy. Also my temp gauge pegs all the way to "H" but i had a shop check it out and the car really runs cold. They said its a electrical problem. Also When I shift gears the car bucks pretty bad and its really bothering me. My best guess is the Alternator is toast and is on its way out. I have a new battery right now, new terminal cables. I'd just like some other input on maybe another solution. thanks.

Yeah i'm gonna have to take it too like autozone and have them check my alternator, my battery is bran new "only about 3 months old" When stopped at night, when i press the brake pedal the lights dim and I can hear my fuel pump slow down, release the brake and its back to normal. its becoming a real problem now though, the car runs terrible, i can floor it and i have NO! power at all just lags and can hardly reach 3K.