Sorry - but eating and driving is just as dangerous as talking on the cell phone and driving. You have already stated you are a nervous driver. I would pack a lunch to eat in the parking lot NOT while driving.
Your lunch bag should be insulated and with an ice pack so you can keep your food cold. There are soo many selections out there now in lunch boxes that you can find a pretty neoprene one that looks like a purse!
lunch meat on a tortilla and rolled up. (yes, I saw that you don't want lunch meat - not sure why would need to heat it up).
Egg salad on a lettuce leaf - rolled up.
Burrito - keep it simple - bean and cheese and if you feel up to it? Add beef.
Fresh Veggies and dressing.
make sure you have snacks that you can munch on - pretzels, cheese and crackers - those are great to munch on and easy to keep.
Apples and peanut butter (not sure if it's just the peanut butter that makes you want to gag or the peanut butter and jelly together).
Yogurt is a good thing as well.
Walk through your grocery store and see what you like and what appeals to you. then go from there.
To keep hassles in the morning to a minimum? Prepare your lunch the night before and keep it in the refrigerator.