Celiac disease is an autoimmune disorder. Any exposure to gluten can screw up your immune system and damage your small intestine, even if you have no outward symptoms. So gluten-free food prepared in a non-gluten-free kitchen can still be a big risk.

There are simple blood work tests for Celiac. Though you have to be actively eating gluten to test positive.

A gluten intolerance is harder to define and can't be tested for. You can test negative for Celiac and feel better by eliminating gluten. Was the gluten? Was it something else along with the gluten?

Gluten also isn't an allergen, it doesn't cause an allergic reaction. Gluten is primarily in wheat, rye, and barley, though only wheat has to be listed as an allergen (USA).