Not celiac here but definitely gluten intolerant/sensitive. I experience the same with certain "sticky" foods (like melted cheese) getting stuck and it's just downright awful.

If you're looking for a little extra reading I highly recommend "No Grain, No Pain" by Dr. Peter Osborne. It's the most in-depth and comprehensive book I've found to date and really explains everything from the science to what foods are on the can and can't list. Here's the link to the kindle version if you're interested: https://www.amazon.com/No-Grain-Pain-Eliminating-Chronic-ebook/dp/B00UDCHX4Q/ref=tmm_kin_swatch_0?_encoding=UTF8&qid=&sr=

I'm not sure what was in those burritos but if they were of the bean and cheese variety, those could have been the culprit. Best of luck.