OK, looking at your photos, it's clear you have built your addition in the middle of the natural drainage draw, blocking the water from it's desired exit. There are several solutions, one would be to install a yard drain and run it around the addition, another would be to bring in fill and fill up the depression. One possible problem with the latter is that I don't know the status of the material under the lawn, does it drain well, or does the water hang there forever and a day? If it does drain well, the extra fill should work just fine, if not, some sort of a cistern may be needed. Another caution, if you are going to rely on infiltration, be sure it is over 100 feet away from the nearest part of a septic system and 75' from a well (or more, depending on local codes. My PE doesn't extend to GA!)
If you go the fill route, you might be ok even if the soil doesn't drain well, just make sure the fill is graded to shed the water away from the house.
This could be a job for Bubba, though the thought of him on a bulldozer near a house gives me the cold sweats.......