I got a DUI in October of 2018. I live in New Mexico. Can I apply for Drivers License in New Mexico.

I am pretty sure it will have an effect on your New Mexico license. You will probably have to comply with New Mexico's relicensing process for someone convicted of this crime. In my state, for example, you would have to present an SR-22 form from your Insurance Company proving you had insurance and you would have to maintain the SR-22 for 3 years or your license would be suspended. You can talk to an attorney in your state or you can ask your DMV yourself about this.