The best method you can ever use is a licensed Texas Realtor. It, normally, doesn't cost you to use a Realtor to purchase/lease a property. And they can arrange a direct and free email search for you that would be directly off the MLS and as up to date as the real estate data base can provide. However, if you really want to look for yourself, check out Redfin.
It is pretty good about staying up to date. There is also an app for Redfin. Stay away from most of the others as their data is frequently old and you would end up hoping for a property that was sold or leased weeks or months ago.