If your other things like iron are fine, it doesn't sound like a false negative on the coeliac test, which can happen. But there are other intolerances. My son is intolerant to FODMAPs, while I'm coeliac, so we went the distance making sure it wasn't that as his chance is higher.
FODMAPs are basically sugars that exist in fruits, vegetables, grains, milk, etc. They're everywhere. It includes cereals containing gluten, lactose, soya, onions, garlic, peas, legumes, pulses, apples, stone fruit, etc, etc. I could go on. But removing those from his diet means he's now healthy, happy and free from pain and other IBS symptoms.
So I'd recommend getting Prof John Hunter's book Irritable Bowel Solutions, which walks you through an exclusion diet to work out what may be causing issues, with a full list of foods to test, explains the FODMAP thing better than I can in a short post (basically, the sugars are fermentable and for those affected they are fermented in the gut instead of being properly processed, hence wind and pain etc) and give you a place to start finding out what works for you. It's worth every penny I've spent replacing the book when friends have borrowed it and not returned it :)
There is hope in sight, and that book is the best resource I've ever seen to help you get there 