Well, no and yes. Texans preferred a "Lone Star" version of every flag pattern flown in Texas or afield. But rather than carry the Texas flag, which was indeed broken out and displayed during the "Secession period" (just after leaving the Union), Texans made Texas versions of official Confederate patterns. Particularly popular was the "Lone Star and Bars", which was a Confederate First National with a single huge white star (as depicted in the Antietam reenactment of the film Glory), or alternatively with a large white star in a circlet of six, or 12, or eight smaller stars, and sometimes with four red stars in the corners of the union, for the Four Civilized Tribes of the Indian Nation after they declared war on the United States.
Texas regimentals carried later on tended toward what was later called a "Texas pattern" of the Confederate Battle Flag, which was shown with or without white fimbriations and sometimes, in the "Taylor pattern" and the Polk divisional flag, with colors reversed. (The "Polk Battle Flag" was also different in being based on the Cross of St George, upright and showing a red cross surrounded by white fimbriations). Texans fought under all these flags and the ANV square version as well, which was occasionally issued to a Texas regiment to replace a shot-up homespun original. Two regimental "Texas pattern" flags were supposedly cut, at least in part, from the silk wedding dress of Texas Senator Louis Wigfall's wife and were called "Mrs. Wigfall's wedding dress" flags. The flags were carried by the First and Fourth Texas Infantry, and the Senator's daughter Louise was also named Fille de Regiment by John Bell Hood himself, commander of the Texas Brigade. His letter to Miss Louise informing her of the honor is still extant, as is at least one of the flags.