The Civic Center in Amarillo/Potter County is providing vaccines regardless of state or county residency:
https://www.texasstandard.org/stori...llo-vaccine-rollout-reaches-beyond-panhandle/
There was an article a couple of weeks ago in the Santa Fe New Mexican newspaper that estimated more than 400 New Mexicans had obtained vaccinations in Amarillo. I don't consider it appropriate but most of those interviewed were in their late 70's, had close ties to Texas, and were frustrated at the slow pace of vaccination in NM. The 1B 75+ became eligible on Jan 10 in NM and less than 50% currently have their first shot. There is a state vaccine registration system with eligible persons selected at random for appointments - nothing you can do to be selected earlier. Now 1B age 16 to 74 with chronic conditions are also also eligible (about 30-40% of the state population) and the Governor seems to be adding in even more groups. Healthy baby boomers are way down the list after many essential workers, including teachers who are heavily lobbying to be re-prioritized.
The Amarillo mass clinics are first come first serve and have been delayed or cancelled a couple of times so you are taking some risk to drive that far (4 hours or more). If there were appointments available, it would be tempting to try to get one. I would be okay with the drive and just stay in a motel overnight.