Why have the corners of my toe nails turned black?

To me, your problem was an external pigmentation.
Black toenail is a brown or black pigmentation of the nail plate caused by existence of excessive melanin. My recommend that you to visit Podiatrist, who will advise you about black toe nails.

Toe nails turning black can be from a number of things, one of the more common causes are that athletes quite often get black toes from running down hill and the toes hitting the end of their trainer, if you have hit or dropped something on the toe it can cause a blood blister under the nail which needs to be relieved. Poor fitting shoes can also cause this problem, sometime toe nails can go a yellowy colour which can be removed if you buff with a nail file.
Best wishes
Janet

Hello, without seeing them it could be a number of reasons. It may be that you knocked those toes, you are wearing new shoes which press or the dye has come off under your nails. Or when they were clipped it caused the nail plates to lift slightly (trauma) and this will grow out. As a beauty therapist we can never diagnose any condition, only say it looks like it may be ... and then suggest you have it checked out by your GP, which I would suggest that you see.
Best wishes
Sian Rogers