The only issue with getting your own luggage when flying SW, but using DME, is the distance you'll be traveling at the airport. You arrive on Side A, on level 3, so you will have to go down to level 2, baggage claim, on Side A, and get your checked bags. Then back up to level 3, cross over to Side B and down again, past level 2 baggage claim on Side B, and on down to level 1, ground transportation where DME is located. That's a fair amount of walking.
You should be fine with DME grabbing your stuff. As noted, you will have what you need for the night.