What is this insect or worm?
Some species of Eupithecia perhaps. A type of moth, the larvae tend to resemble twigs. According to this relatively old text, Eupithecia miserulata is the most commonly distributed species in Texas, but I'm sure identifications stem largely from expertise and adult specimens, both of which I lack. The larvae for E. miserulata don't seem to visually match what you have, there. 

In essence, though, it's a caterpillar that will turn into a moth.