Depending on the size of the "mess", maybe a ceiling light medallion would cover it.
You might also remove the popcorn around the light in a circle or oval, and paint a medallion. Spray with warm water and scrape it off. https://www.youtube.com/watch?v=d1yf-IeLGBI
You could also make a large drum shade to put on the light fixture to hide the mess if its not too big... https://www.youtube.com/watch?v=lWcFzij9II8
Home Depot sells a repair in a can for pop corn ceilings you spray on