How long ago were you diagnosed?  Many people with celiac disease, especially those who are in the 0-2 year range of their recovery, have additional food intolerance issues which could be temporary. To figure this out you may need to keep a food diary and do an elimination diet over a few months. Some common food intolerance issues are dairy/casein, eggs, corn, oats, and soy. The good news is that after your gut heals (for most people who are 100% gluten-free this will take several months to two years) you may be able to slowly add some these items back into your diet after the damaged villi heal. I had a half dozen or more temporary intolerances until my gut finally healed, and after than I was able to add back most foods (except gluten of course).  

Let us know how it goes.

The doc that diagnosed me emphasized that the ears, eyes, nose, and mouth all drain to the same place. He said, besides obviously not eating foods containing gluten, to eliminate flours from my world immediately. If gluten flour is used, it gets into the air, and would be breathed in through the nose, which drains down to the stomach. Also, if it gets into the air, it settles on everything, which would be very difficult to clean. So you are correct to be concerned about flour in the kitchen. Some people may argue this isn't necessary, but it was my doc's advice, which was 10 years ago. My step granddaughter was diagnosed with celiacs last year and she got the same advice at a post-diagnosis nutritionist consultation in Seattle.   

Cristina, it’s possible you may find other foods that also give you the same reaction. My advice: make a list and stay away from them.

Funny you should mention this.  Three times in the past I've had a similar reaction to glutening when I eat broccoli. People have suggested I try it again to make sure it is the problem but I have three distinct memories of meals containing broccoli which caused chills, feeling sick and diarrhea within an hour or two of eating (and this was before I was diagnosed with coeliac disease).  Because I reacted in such a way, I have no intention of giving it another go!