well, I know they say rice is easy to digest but I can't tolerate it either nor potato. I get a rumbling tummy and tiredness amongst other things. I don't have celiac disease though.
I'm also allergic to cats, sadly I had to give them up because the products on the market didn't work for me.
When my children were younger I took them to a health shop that did a sensitivity test. You hold a ablong shaped piece of metal and I think it measures your strenght to a lot of foods. It costs about £40.00 that's with a vitamin and mineral test and it's totally harmless, no blood is needed.