Kuntz & Pelliccioni's Traditional Tune Archive dates the common fiddle tune to the 1925 recording by Gid Tanner & the Skillet Lickers.

A recent performance: https://www.youtube.com/watch?v=1r_bnyr0HaM

No old printed version of the tune seems to exist.

There is, however, at least one other tune with the same title. This was recorded in 1925-26 by native Georgian Fiddlin' John Carson.

A recent performance: https://www.youtube.com/watch?v=Sf1AjBOpP5o

(Carson's track is barely audible, but the above sounds to me like what he's playing: https://www.youtube.com/watch?v=8TXcam0HGQQ )

The earliest mention of a tune by this name appears to have been in a diary entry of Feb. 17, 1870, noted in Decatur, Ga., by Civil War veteran George W. Bailey. There are two much later but presumably reliable claims that "Hell Broke Loose in Georgia" was known during the Civil War.

I've always felt that the Skillet Lickers' tune sounds too modern to have been played in the 1860s. It has suggestions of the turn-of-century "Chicken Reel," plus a notable ragtime shuffle.

Carson's tune has the advantage of being, I think, a better fit for the words "Hell's broke loose in Georgia!"

So it may be more likely to be close to the "original" melody.

The Traditional Tune Archive gives a lot more information about both tunes.