Does oatmeal contain gluten?

Maybe not: Oats and oatmeal are listed as a gluten-containing grain. More recent reports say that oats don't have the gluten proteins but have small amounts of another protein that may cause reactions in some celiac disease patients. Sometimes the same equipment that processes oats also processes wheat, so there can be traces of gluten from the wheat getting into the oats. So, "pure" oats probably are ok.

Yes: Oatmeal contains gluten.