No, but I wish it was!
Yes, as a celiac I must be gluten free, unless I want to be in pain!
Gluten is in wheat, barley, moult, and rye. Wheat is just wheat.
Corn contains corn gluten. Corn gluten does not contain Gliadin, which is what people with Celiac Disease are intolerant of. If you have a corn allergy, then you have to stay away from corn, too....
All real milks are gluten free - gluten is a cereal protein.