Ha. I have to admit while I don't technically have to wind it (at all) I still find myself doing that as well. Pick it up... wind it a prime number of times... put it on for the day.
Symmetry fixation thing. I sort of used to have to do most things an even number of times. Wind the watch. Pushups. Jumping jacks. Whatever. Anything that required a count. I switched to counting to a prime 3 or greater and the anxiety just went away. Been doing that for years now. Took me awhile to realize I was even doing it in my head... and luckily the fix was pretty easy.