Maybe it's a "least flycatcher"? They're sparrow-sized, according to my bird book, but they supposedly only migrate through TX, rather than living there full-time. Most of the flycatchers in my book have whitish breasts, but with an "unbuttoned gray vest" and darker gray "coats" with white or lighter gray wing bars...
Swallows are also sparrow-size, or thereabouts. Barn swallow has a really pointy forked tail and some yellow and brown markings around the throat. Bank swallow is creamy white underneath, brownish above. Tree swallow is dark gray or blueish above and white beneath. Chimney swifts are charcoal gray with white underneath. They have a really short, stubby tail, while the barn and bank swallows have shorter tails with V's in them...
Any of those sound close?