A high percentage of celiacs can't tolerate dairy and they react to it like they do gluten. I would suggest a trial of removing that from your kid's diet for several weeks to see if symptoms improve. Same with oats, even gluten free oats, contain the protein "avenin" which is similar enough to gluten that it causes a gluten-like reaction in about 8% of celiacs. Some cultivars of oats actually contain gluten.

My kid has been eating gluten free (taking care of cc too) but he has constant stomach pain since diagnosis (4 months) Was wondering to look into other food allergies?

It depends on what kind of allergy testing you want done and whether or not your insurance will allow you to make direct appointments with specialists. Serum allergy tests can be ordered by a PCP using a blood draw. Epidermal "prick panel" allergy testing would need to be done by an allergist. There is also something called ALCAT food sensitivity testing. We use the term "allergy" rather loosely and differently than it is used in medical settings.  All food allergy/sensitivity testing is problematic and the results often do not agree with each other or with actual symptoms. It's worth doing some research as to reliability before you dive into it.

How do you do allergy tests? The primary doctor sends you to an allergist?

1/1/2 slices of bread is likely not enough. Current guidelines for the gluten challenge are recommending 10g of gluten daily which is about the amount found in 4-6 slices of wheat bread. Physicians in practice are often working from outdated info.