CAD
I think you are correct in not ignoring this.
Just be aware that many celiacs thrive when they can identify the other foods to which they are sensitive (not allergic, so they won’t show on a standard allergy test).
And studies show that usually dairy is an issue with absorption as well (you can research this online).
When you solve any other malabsorption issues and remove them from the diet (trial and error, or alternative), your child should thrive be”H.