If possible register the car in New Mexico in your name once you get the NM Drivers License.
If you don't have your own car and you get pulled over in Texas you can always say you're on vacation and your relative let you borrow the car that should work.
__________________
Packet Sent: 11/13/12 (USPS Express)
Delivered: 11/14/12 11:55am
G1145 Txt: App accepted 11/19/12
Service Center: Nebraska
Biometrics: Recieved 11/28/12 (notice 11/21/12)
Appointment 12/13/12
Walk-in 11/30/12
Approved: 5/30/13
EAD: 06/05/13
SSN: 6/13/13
Renew DL: 07/02/13