My nail has a line from the bottom of the bed to the white part. Everytime the nail grows, it splits in that placeHow do you fix a split cuticle and nail?
It sounds like you damaged the nail underneath the skin. I'd think that eventually it would stop doing that--you don't say how long it's been happening.
One thing you can do is take apart a teabag and use some clear nail polish to apply the teabag paper like a bandage across the split. It will look a little lumpy so you'll have to paint your nails to disguise it.
Or you might want to go to a nail salon and see what they suggest.