You most likely have a sharp edge on the nut either at the front (most likely) or ta the back. Take off the strings and get a magnifying glass and look at the string slot. Get somehting hard small and pointy (toothpick) and slide it down the string slot and see if it catches on the lip wither in the front or back. If it catches you will have to sand down the lip, be careful to keep the string slot at a right ange to the edge. You only want to get rid of the sharp bump up. You want a clean 90 degree edge with no burrs. If you have the string slot slope downwards and end up with a greater than 90 degree edge you can get bad buzzing and no sustain on an open string.
Use 400 or 600 grit sandpaper very lightly or if it is a large lip and you are careful, you can shave off the lip with a straightrazor and dress it smooth with the sandpaper. Just go easy and check it often with the mangifying glass and toothpick. Clean everything well so you don't leave any grit.
You ought to check the other stings around the vicinity of where they exit the nut to see if they are nicked. You might have a smaller problem there also.
A trick I learned is to take a sharpened pencil and rub it on the bottom of the string slot to lubricate the strings and help not to damage them when youi reinstall.
Just remember to keep the edge square and work slowly, while checking often. GOOD Luck