I think the professor's remarks were also unprofessional, but that doesn't make hers any less unprofessional. Think about how the complaint would read and I can't find a way to word it that comes off looking reasonable.
Dear Dept Chair,
I have an issue with Prof. Plum that I'd like to bring to your attention. I referred to patients with severe mental illnesses as "nutjobs" in class during a presentation and he called me out on it in class. I think it was inappropriate and he should have waited until after class to do so. When I wrote an email to him later telling him that I would need to miss class because of a health concern and reiterating my apology for using the inappropriate term in class not only did he not tell me he hoped everything was okay, but he also further reprimanded me for using the term. I consider this highly unprofessional behavior.
In fact, this is part of a pattern of his. Previously in class he referred to "hysterical women" and made derogatory concerns about southerners. For example, when a student presented on women's health research in class, he made jokes about women being "hormonal". The first time he made the joke we all laughed as it seemed he was being sarcastic/satirical, but then he proceeded to interrupt her presentation to make the same type of joke two more times, which got less funny and more uncomfortable each time. Also, he has referred to negative stereotypes of people in the southern U.S. before, such as that they have names like "Billy Bob," are uneducated, all carry around shotguns, etc.