Yes, those are the shavings.
Coarse hold up better to mud than fine, but neither is as good as wood chips.
The reason that the wood chips hold up better is that they don't pack and mat so readily -- allowing airflow that evaporates water and facilitates aerobic composting organisms rather...
In Georgia I suggest pine straw.
It's not the most absorbent bedding, but it's highly resistant to packing/matting and dries out quickly on top after even the heaviest rainfall.
If the area collects standing water because the drainage is poor then no bedding of any kind will ever prevent mud.
Fixing the drainage can be difficult, laborious, and/or expensive, but if the coop and run are in a low spot where puddles collect then there's no other option.
If nothing else, try putting down some pallets and/or straw bales just to give your birds a dry place to stand.
Do your garden centers have bagged mulch yet? The coarsest plain, undyed mulch you can get might help.