Oz, that's a good question. Perhaps one of our community members that has COPD will chime in with their experience with this.
I would certainly recommend that you ask your doctor about it next time you see them. Sometimes a person can get a red face if they're struggling to get enough air - have you noticed if that's when you get red? Excessive coughing can also cause a person to get red in the face.
Let us know what your doctor says when you see them.