I have a problem with things near my eyes.
Ditto. I can't stand eyeliner or mascara for that reason.

As for other strange hang-ups, there are two related ones that come to mind. I cannot sleep wearing long sleeves or pants. I don't care HOW cold it is. I also have a hard time sleeping without a blanket of some sort, no matter how hot it is. Seriously. It can be 90 degrees, and humid and I'll still sleep under a comforter. (and a fan, which drives my grandma up the walls) Don't ask why, I don't get it either.