you could go out on a limb and ask for plain white rice instead of the mexican rice. Although I did that one time and the woman looked at me like I was an alien or something......but its worth a shot!
You did great!
My fave Mexican restaurant dish is vegetable fajitas and I say "no tortillas, please." Or I get the chicken fajitas and ask for them to add mushrooms and broccoli and NO tortillas, extra lettuce. Eat it with a fork like a salad. Yummy!