I rock and sway back and forth all the time. No clue how to tell if I do it when walking, lol, but I know for some reason I cannot walk in a straight line and am constantly walking into people, so I wonder if maybe I do a swaying motion somewhat when walking as well.
It soothes me at times, when I'm overly stressed or in an uncomfortable/new situation. At other times I tend to start swaying a lot when I'm excited about something that I'm talking about.
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Sorry for the long post...
I'm my own guinea pig.