Years ago (15? 18?) I dropped a steel door on my running-shoe "protected" big toe while taking it off the hinges.

(Hey, everyone, wear steel-toed boots!) The sharp lower edge cut/squished the nail right at the bed, and the doc had to put a couple of stitches in. Since then, the nail look fine until about half-way out, where it seems to "delaminate" into several layers. You probably damaged your nail bed too, and since the cells that make up the bed aren't quite what they were before your boo-boo, that's the way it grows now.