Is what the wife said, out of fear of ẓihār after telling her husband when he asked to change their son's shoes, "He is wearing good shoes," or her telling another person when a previous problem occurred with her husband, "I cannot leave my husband, for he is my father, my brother, and my friend," considered a form of ẓihār, knowing that she suffers from obsessive-compulsive disorder?

You are afflicted with severe waswas (definition) (obsessive whispering/doubts). You must turn away from it and not dwell on it. What your husband said to you and what you said to each other, describing each other as "my sister" and "my father and my brother," does not constitute a divorce, nor zihar, nor anything else. However, it is a statement that should be avoided, as it is from the speech of foolish people. It is worth noting that a woman cannot issue zihar or divorce. Take it easy on yourself and try to treat the waswas, and increase in supplication (du'a) and seeking forgiveness (istighfar).