<human>: Condense the text into a few key points

This actually happened a week ago, but I stilled worried to death about it. Sorry about the wall of text.

I was called to the professor's office, regarding a econ midterm I took not too long ago. The prof wanted me to explain how I did one part (out of 4) on the one free response question. I know I didn't cheat, but I did make a really bad arithmetic and logical error. I put the incorrect work since I mixed up the quantity, but got the right answer. My neighbor's version had the same quantity that I input. Other than that, I basically got the rest of the test right. 

I reasoned with my professor that I had a massive brain fart, and that it would be highly illogical for me to copy part of a free response, when there is already 4 different versions of the test out with different numbers for the one free response question. Other than that, there is no other concrete evidence pinning me as a cheater.

Prof didn't believe me and now has sent a report to the dean. I'm awaiting the dean to contact me, and the anxiety is affecting me mentally and academically. A family friend wrote a letter on my behalf, but it was made clear that this issue was between the school and me. I'm not sure what to do, whether I try to contact the dean myself or try to get a prof to vouch for me. I'm scared out of my mind that I'm digging myself in a deeper hole than it already needs to be.

What a great way to start the freshmen year on the first quarter, right?
<bot>: took a midterm. went "the math checks out" on a part of a question. caused the prof to accuse me of cheating. now I have to see the dean and no idea what to do.