These native Texas trees have other common names, including Sand Plum, Texas Plum and Texas Peach Bush. The peaches you see in the grocery store are also members of the Prunus genus, but Prunus Persica, which is the commercially grown peach, is native to China and southern Asia.
If you grow the Prunus texana (Peachbush), you need to remember that all parts of a Prunus are poisonous except the flesh of the fruit, and even in that, the seed is poisonous. In other words, a Texas peach bush shedding leaves or twigs could be a poisoning danger to pets or livestock. We could not find any information about the taste or texture of the fruit of this plant. We suggest you contact the Texas A&M Agrilife Extension for Bexar County. County extension offices tend to have more information on raising edible plants. There is contact information on that webpage.