Moving to and from the vehicle you're ok.
Once you're in the vehicle it has to be in a "two step" container. IE, something that requires that you activate a latch, and then open it. Gloveboxes, center consoles, trunks, etc all pass this test. It can be kept loaded in those areas.
Concealed carry doesn't reciprocate with GA as noted, and SC does not honor any non-resident permits.
Open carry is not allowed except while hunting or fishing (or driving to/from your place of hunting or fishing) with a valid license.
You're fine to keep the gun loaded in your residence and we have castle doctrine.