I've never noticed a problem with any type of soda that I've had. My tastes run to diet cirus flavored sodas, like Diet Sunkist and Diet Squirt.
Some people report that they have trouble with cola flavored sodas, it is usually thought that the caramel coloring may be derived from wheat. From what I've read, almost all caramel coloring used in the USA is derived from sources other than wheat, and should therefore be OK. Pepsi Cola and Coca Cola are frequently reported as stating that their caramel coloring is OK.
Some people don't seem to tolerate Aspartame very well. This might be completely unrelated to celiac disease, and just be some additional sensitivity you have developed because your digestive system has been stressed by autoimmune reactions.
I'd just lay off the soda completely for 6 months or so, then see if it still bothers you. Just a suggestion
