This answer assumes that you'll be planting ornamentals, not vegetables. If you're more interested in vegetables, then I would relocate the garden and not try raised beds in that area (after all, would you really like to slog through that muck to pick veggies?)
For ornamentals, another version of Peter's quote is really landscape design 101: "Right Plant, Right Place." So, since you have a wet mess after rains, you might be best served by planting things that like living there: in this case, I would look toward a rain garden rather than a bog garden, given that there are far more varieties of plants available for the former.
Here are some sources, if you're interested in exploring this option:
The Vermont Rain Garden Manual
Don't let the location in the title put you off: this short manual discusses all facets of site selection, sizing, installing, and maintaining a rain garden, all within 9 pages. The rest of the manual is Vermont-centric, so probably won't apply to you.
Mississippi State University Extension Rain Garden Guide
A short discussion of rain gardens, including sizing, along with a short list of Mississippi-specific plants appropriate for planting in a rain garden.
Clemson University's list of plants for wet places
The plants in this list should be zone-appropriate for Mississippi, although the summer humidity on the Gulf Coast could could be a factor in a plant's survival.