Hi I'm from St. Bernard but now live in north MS. I really don't have a good answer for you about the drainage but will share my experience with a wet yard up here. First look at the way the yard drains. Sometimes the ground is uneven which was one problem with us here, and I shoveled and leveled it some, not a really big project (I weigh about 111 so it wasn't heavy work), and that helped alot. Also sometimes there is a fence or blocked up area that has to be cleared of debris. That was the case for us too. I then used raised beds, not made of timbers but just mounded up and dug small trenches as borders around the beds and so the plants stayed much drier and the water that didn't drain sort of ran in the trenches. If I am picturing a flooded yard I don't think most plants would absorb that much water but maybe a tree like river birch would. One other thing, when we get a huge rain like this week 4 inches in 3 days, that is just a one or two day yard drenching but then it does drain. Hope this made some sense or gave you some hope. To truly solve a drainage problem might need a landscape contractor. And if you rent then perhaps the landlord/lady will fix it.
Laurie