mesquite
Barberry
prickly shrub
Oleaster
An Apache plume is a desert shrub of the Rosaceae, which grows in the southwestern US and northern Mexico, Latin name Fallugia paradoxa.
Chaparral is a thorny shrub native to North American prairies.
It is a creeping rhizome shrub with branched thorny whitish stem.
Sounds like a Berberis.
"Cotulla" is a Spanish word that can refer to a type of shrub or small tree found in the southwestern United States and northern Mexico. It can also be a place name, such as the city of Cotulla in Texas.
The Ocotillo is a V-shaped woody shrub with cane like stems that rise upward from the base of the plant. It is widespread throughout the Southwestern US, and the Sonoran region of Mexico.
An aspalathus is any of the genus Aspalathus of flowering plants, or a thorny shrub yielding a fragrant oil.
A barberry is a thorny shrub of the genus Berberis, which bears yellow flowers and red or blue-black berries.
The Kangaroo Paw is a native Australian shrub which is found in southwestern Western Australia. It prefers a drier climate than that found in the east. Its habitat is sandy soil in grassland and semi-arid areas.