I don't know much at all about the Coosawatchie battle. It was part of the March to the Sea/march into SC with Sherman and it was north of Savannah, GA. If you have access to books on that campaign they should cover this engagement. The Official Records will have reports too.
I have not heard of the other site you mention.
The flag of the 3rd Georgia Reserves is at the Museum of the Confederacy in Richmond.