This is indeed an unknown Georgia flag. The ones I have seen with the state Coat of Arms do have the unit names on the reverse side. Several flags of this style still exist mostly in smaller museums in Georgia.
I have been working on a book of Georgia Civil War flags for 12 years and still have a few more to go - and I have to get the Tennessee flags book done first.
Georgia was one of the Southern states that did not adopt an official republic/state flag. The only officlal republic/state flags for the South were South Carolina, North Carolina, Virginia, Mississippi, Louisiana and Florida. These were adopted by acts of their legislatures. The Texas flag of 1839 which had fallen out of use prior to the Civil War, came back into wide-spread use.
Tennessee considered a flag and it did not pass. It was modeled on the Confederate First National (like Florida did). Arkansas, Alabama and Georgia did not adopt official state flags. The rump states of Missouri and Kentucky also did not have official state flags but both had units that used their state coats of arms on flags. The Confederate Missouri State Guard used these flags in the early war, for example. Some were made for them in Memphis, TN.