This sounds like Rhus copallinum (Winged sumac). They have winged stems, grow quickly and often form colonies from a single plant with a tap root that has rhizomes that produce sucker plants, making a clone of plants. Here are more photos and information from Illinois Wildflowers and University of Florida Lee County Extension.
The fact that your plants may be all connected is going to make them a bit more difficult to eradicate. To be rid of them you will need to dig them up. To help you get rid of them, you can carefully treat the broken or cut remaining roots with herbicide by painting the surface of the cut using a small foam paint brush. If you do use herbicide, be sure you read and follow the safety instructions on the label and be careful not get any of the herbicide on plants you want to keep.
For another possibility, there is an Asian plant, Euonymus alatus (winged burning bush), that is considered invasive over much of eastern North America. The Invasive Plant Atlas of the United States shows that it has been reported in southern Oklahoma, but not in Texas.
And here are photos of other plants with winged stems from the Native & Naturalized Native Plants of the Carolinas & Georgia website.
By the way, it's Smarty Plants (not Pants)!