I live in NM too and it took months for me to get a cancer diagnosis. Most of tests/consults were at least 75 miles away from where I live. My suggestions:
get on waiting lists for cancellations
try Los Alamos (good level of care) and Espanola (availability through Presbyterian)
***And yes, do go out of state. NM is very poor and very underserved. I'd go to Colorado or Arizona (Mayo has a branch there). I know it might sound ridiculous in a densely populated place that has resources, but not for us. I've always been careful to have insurance that covers out of state. See if you can get a tele-medicine consult too. Many of my friends and family immediately leave the state for anything complicated--in particular go to Denver or to Scottsdale. I wish you the best.
I'm so lucky to live in our gorgeous culturally rich state, but have always known this was a drawback. Other people come here for vacation--we have to go elsewhere for medical needs.