Since New Mexico is a fault insurance state, only an at-fault car accident will negatively impact your auto insurance. If you were not at fault for your hit-and-run accident, it will not affect your insurance. Your premium will not increase as a result of filing a hit-and-run claim, as long as you can provide a police report.
However, you may have to pay a deductible to receive payment for your medical bills and property damages. Hit-and-runs are the only accident type where you will still have to pay a collision deductible, even though you were not at fault (in most cases). You will only have to pay a deductible on vehicle repairs, since no other insurance company is available to pay off the debt. The rules will vary according to your insurance company.