Does Botox Move Around?

This is a very unusual complaint and may be due more the underlying muscle rather than the Botox itself.

we can't inject botox too close to the eyebrow at the outer aspect as it may lower the eyebrow. The muscle of the forehead then still functions and can pull upon that part of the eyebrow but the middle of the forehead doesn't come up since we can treat the region between the eyebrows.  Sometimes we inject the crease you mention with filler and try to use a very small amount of botox above, not in, the crease. See your doctor to evaluate what can be done to adjust it.

I am not sure what you are seeing but Botox is fully taken up and set within a couple of days. The duration of effect is the body's time to restore the muscle function, not the Botox itself. Occasionally adjacent unaffected muscles are "recruited" until the injected muscle works again, perhaps you are seeing something like that.

It depends on how concentrated the solution is that is injected. If it is a heavily concentrated solution of BOTOX, it doesn’t move at all.

Botox does not move around after administered.  What you may be seeing is some muscle activating to compensate for the brow paralysis. This could be from the orbicularis muscle around the eye.