Is it unethical for a professor to misrepresent the format of an exam? If a professor at a university explicitly states an exam will contain "multiple choice questions and true/false questions" and then administers an exam with several short answer and essay questions, is that worth filing a complaint to the department about?

I'm a very dedicated student and don't mind essay questions at all, in fact, I prefer them...when I've been given proper notice and can prepare accordingly. There's a much different way to approach material when you need to draft responses from memory. If it WASN'T clearly stated what the format of the exam would be, that would be different. If it were one or two questions that deviated from the format, that wouldn't be a big deal. But to clearly state it would be multiple choice and true/false and then to have about 20% of the exam not follow that format seems unprofessional and poor practice. 

I've already reached out to the professor about it and have not yet received a response. However, I'm considering also contacting the department. Am I overreacting? Or is this reasonable?
First, there’s some important background information to consider about professors, which is that they are human and occasionally make mistakes just like everyone else. In particular, as can happen to anyone in any other workplace or general life context, they may sometimes forget what they said to whom and when, or say something they didn’t fully intend, e.g., omitting an important detail or making a statement that is misleading or not entirely accurate. 

Moreover, these effects are at their worst when a professor is overloaded with work. Small misstatements of this type can happen for example because a student accosts them with a curveball question at the end of lecture when they are frazzled and distracted and in a hurry to get somewhere (happened to me more times than I count), or due to many other kinds of cognitive overload that are a frequent occurrence in many professors’ lives. As an example, just this week I confused the lecture times of the two different classes I’m teaching in an email to a colleague about scheduling a meeting, and have found myself making a few other similar (fortunately insignificant) mistakes recently. This is very atypical for me, and it’s clear to me that it’s strongly correlated with a period of increased workload.

Coming back to your question, it’s obviously not great that the professor did not give you accurate information about the exam, but saying it’s “unethical” is making a statement about the professor’s intent. If they deliberately misled you, then yeah, that’s not very nice, and, depending on how misleading their description was, I can see the label “unethical” as being potentially appropriate. But based on my experience, I’m extremely skeptical that the misrepresentation was intentional. It’s much more likely that the explanation involved an error, forgetfulness, preparing the exam at the last minute and making a spontaneous decision to add an essay question without realizing that this would make some students upset, or some other such explanation. 

Basically, in most situations of this type in academia, rather than assume bad faith, your default assumption should be that the person whose behavior you are aggrieved about made a mistake. They may be disorganized or even mildly incompetent, but none of that equates to being unethical. Unless you have hard evidence of an intent to deceive or the level of incompetence implied by the mistake is truly outrageous, complaining about this seems like a waste of time to me.