Professor complaint

I have a professor that is just an absolute mess. I could explain everything, but this post would be so incredibly long.

Suffice it to say, I have finally decided to discuss the issues with someone. My understanding was that the correct person to reach out to was the head of the department. I emailed him a few days ago and have not heard back.

I plan to follow up with an email that basically says, "if this isn't the right avenue, I'd appreciate you pointing me in the right direction."

Unfortunately, I have no idea what I am doing. I have never been in a position like this before. I have had some professors I haven't liked or thought were bad, but I have never before felt like someone needed to be alerted.

Please don't make assumptions about my motives; I have an A in the class. The class is not difficult for me and I have self-studied the whole way through it. I'm not upset over a bad grade or an unfair exam or blaming a professor for a difficult course. Someone just needs to know how this professor operates. Hopefully, somebody can guide her to do better.

What do I do if the department head just never responds to me? What are the next steps?