I know almost nothing about Tomball, but I do know some research tips that may help you find the information you're looking for.
First off, about Red & White: R&W was a franchise chain, and its name was typically subservient to the name of the individual owner (i.e., "Bill's Red & White"). Many of the stores that did business under the Red & White name did so only briefly in the 1960s and 1970s after longer tenures as completely independent grocery stores, and later switched to other franchises or went out of business entirely.
To confirm the names and locations of historical businesses, I'd ordinarily suggest visiting the public library and looking up the name or address in one of the hardbound city directories from decades ago. Tomball is so small, however, that I doubt a city directory was ever published. Phone books are less reliable (and sometimes leave out addresses altogether), but sometimes work as a fallback.
Another thought: In small towns that never had city directories published, you can sometimes get a sense of what stores and businesses historically existed by looking for sponsor ads in old high school yearbooks. (This is how I know that a Mick-or-Mack supermarket existed in Athens, WV in the 1940s.)
The Chaparral Genealogical Society
might have some resources that could help.