Carrying handguns is illegal in Texas, and your license is a defense to prosecution. This is the case regardless of what TexasInvestigator chooses to believe.
So, if the cops ask to see your license you are being lawfully detained. He can arrest you for UCW. Show him the license. And if you're going to OC, don't dress or act like a scumbag.
Interestingly, this is the same for a peace officer license.