Another though that comes over me is that it might be a stim. The real difference is that with a tic, it builds up and needs to be carried out. The relief is just from the tic itself.

A stim can help with general anxiety, overload and stress. Stims are often rhythmical or circular in some way (although most mine are not). When I stim I do so my mind will sort of be distracted and busy, a sort of self soothing.

Some only stim when they are upset, some stim when they do nothing else, and some stim when they are excited.

Most stims are "harmless" but sometimes people have self harming stims. Self harming stims are often to block out pain (mental or physical). Other stims can sort of have different jobs.