The song you're looking for is probably YOU DON'T HAVE TO GO by Jimmy Reed. Lots of people have recorded it: The Chambers Brothers, Willie Dixon, Freddy Fender, Freddie King, Louisiana Red, Sam Myers, Pinetop Perkins, The Siegel-Schwall Band, Muddy Waters, and many others, and of course, Jimmy Reed.

Here's one set of lyrics, from http://www.harptab.com/lyrics/ly3801.shtml:

YOU DON'T HAVE TO GO (VERSION 2)
Jimmy Reed, recording of 1961, from "Jimmy Reed at Carnegie Hall" (Suite Beat 3001)

Oh, baby, you don't have to go
I'm gonna pack up, darlin', down the road I'll go
Well, I give you all my money and you go downtown,
You come back in the morning and you call me a clown
Oh, baby, you don't have to go
Oh, baby, honey, what's wrong with you?
Well, you don't treat me, darlin', like you used to do


Here's another set, from http://www.harptab.com/lyrics/ly4634.shtml

YOU DON'T HAVE TO GO
by Jimmy Reed
As sung by Muddy Waters, recording of June 6 1963, from "One More Mile" (MCA/Chess CHD2-9348)

Oh baby, you don't have to go
Oh baby, you don't have to go
You know I'm gonna pack up baby, down the road I go

Whoa baby, what's gettin' wrong with you
Whoa baby, what's gettin' wrong with you
You don't treat me nothin' girl, like you used to do

Well I gave you all of my money and let you go downtown
You come back in the evenin' you call me all kind of clown
Oh baby, you don't have to go
You know I'm gonna pack up baby, down the road I go

Whoa baby, turn your lamp down low
Whoa baby, turn your lamp down low
I beg you all night baby, you don't have to go