I would say that your bigger problem would be safety in general if traveling to Mexico in the near future. Have you read the newspaper or listened to the news in the last week?
I would not recommend going there at all. But if you have your mind made up, I will point out that pipian sauce and most mole sauces contain nuts and so does some, if not all, Mexican chocolate (which could be used in hot drinks and desserts). There’s another dish called “chilies en nogada” that is made with a walnut sauce. Of course there are sweets that also use peanuts such as almendrados and turrones and cookies called polvorones de cacahuate and Mexican wedding cookies. I also just read on Chowhound (from a person who lives in Mexico) that even some salsas contain nuts. I never would have guessed that. This person also said, because of the culture (trying to please) even if you asked if a food had nuts in it, or was made with peanut oil, they would likely say no, even if it did contain nuts.