Oh, yes, I've done this a lot all my life. Always anti-clockwise circles, and on tip-toe if I'm feeling particularly wound up. It's only since coming on the forum that I ever let anyone know I do it (maybe my mum knows, I don't remember when I was really little). And yes, it can be a time when strange thoughts come into my head too. Try to think of it as the strange thoughts finding their way out, so that you don't have to have them stuck in your head forever - I find that if I say them out loud once or twice, and tell myself that I don't want them any more, they quite often do go away.
Sometimes it can help to find something else you can do that works to keep you calm. It is very different for every person, but I find clenching and unclenching my fingers and toes works quite well if I'm in a place where I can't pace without disturbing people. You only need something to help manage the nerves for a little while sometimes - you can maybe pace later on when you have some time on your own.
If pacing gives you comfort, and it's doing no-one any harm, then you should try not to worry about it too much - but as Kraftie says, trying to reduce how nervous you are is a much better solution in the long run.
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When you are fighting an invisible monster, first throw a bucket of paint over it.