I had Botox and three hours after coughed very hard. Could this make my Botox move?

Thanks for your question.  Coughing will not move your Botox few hours after injection.   Enjoy your results. 

Not to worry. Your botox did not move after coughing. You will begin to see the result in 3-5 days with full development at around 10 days to 2 weeks.