Your pottery could be termed "Southwest", I suppose, but it is not Native American, not made in the U.S., and not antique.
This is a figural jar from Mexico, made in the village of Mata Ortiz, in northern Chihuahua. The potters are Mexican, and all have learned to make pottery in the last 30 years or so. In the 1970's, a local farmer, Juan Quezada, decided he wanted to learn to make pottery, and basically taught himself, based on trial and error, and by studying ancient pottery shards left by the Casas Grandes people, who had lived in nearby Paquime from ca. 1250 to 1450 AD.
He made some pots, sold them, they were discovered by an anthropologist in the U.S., who tracked down Juan Quezada, and persuaded him to make more. Juan soon was teaching his family and neighbors how to make pottery, and today there are some 400 or so potters in the village, and Juan and many of the potters are now world famous. Some still make copies of the ancient Casas Grandes pots, which this represents, but most now make contemporary Mexican art pottery.
I suppose there is a remote possibility that this is an original, pre-1450 Casas Grandes pot, but based on what I can see from the photos, it is one of the hundreds of replicas made in Mata Ortiz, which means it can't be older than the late 1970's...even though it "looks" old. (And if it's a pre-Columbian piece, you are potentially dealing with a number of antiquities laws, which you need to investigate before purchasing.) But since it is almost certainly a Mata Ortiz piece. you are simply looking at a contemporary Mexican interpretation of a decorative figural effigy jar.
