Naturally I thought I would try to find out how it happened. I opened the console and typed showracemenu. This fixed the eyes right away so I just said I was finished, renamed my character, and exited. Shortly after I had realized it happened again. The debugger in me decided to do a lot of testing to see what causes it. So far the only thing I found that causes it was the invisibility magic effect. As soon as the invisibility wears off, my character's eyes are messed up.
I guess I hadn't noticed before because this is the first character I am playing that has used invisibility potions or spells.
I know someone will eventually ask for http://www.shanespages.com/Skyrim/miscresources/DxDiag.txt.
