South Texas gets some weird weather. They don't teach you how to forecast for places like Del Rio, Texas in college...you just have to be here and do it enough, gain the experience, and try to make sense of it all.
In most locations through the United States, cold fronts generally pass through in matter of minutes, pushing warm, moist air out of the way and ushering in much more dense, cool, dry air in from the north to northwest. Not in South Texas. It sometimes takes days for this to happen.
In the depiction below, I've shown low-level relative humidity and wind direction, and drawn in high and low pressure. This is from about 6pm this evening. In most places across the country, the cold front pushes through quickly, rapidly changing the weather. This is because the jet stream is "driving" the cold front. In South Texas, however, the jet stream rarely makes it down this far south. It stays further north, pushing the storm eastward, leaving a "tail" behind it, known as a Stationary Front. Like a dog's tail, it likes to wag back and forth from time to time, but never really progresses anywhere. This is what happens in South Texas, and makes weather prediction very difficult at times.
In the picture below, you can see the High Pressure over the Great Plains battling it out with the Low Pressure over the Gulf of Mexico, leaving places like Del Rio right at the edge of the Tail Wagging Zone.