Yes. Carry your license at all times when driving in Mexico. Local liability insurance is necessary and should be included in any rental car agreement. The US or foreign auto insurance will not cover you in Mexico.
Take care when driving through towns for pedestrians and animals. Road markings are not as visible after dark so do not plan on driving far if you are not confident. If someone starts flashing their lights at you, they want to overtake. Slow down at police huts; they will usually wave you through, but may have a couple of questions. Watch out for topes, Mexico’s evil speed, and barely visible bumps, learn what they look like, they are not always sign posted.