Overlapping toenail and Black spot on toe nail

Possibly 2 explanations....you have either damaged your toenail in the past [the black bit looks like old damage] and and the old nail is dying and the new nail is growing under it,or you have a fungal infection.

Try to cut the nail back as far as you can and rub in a softening ointment every night. Vicks vapor rub is good for this.   The nail will gradually grow out and lift off but it may take some time.   You can also try some toenail fungus medication which you can buy in any chemist.   Both methods will take time but do cut that nail back to give any treatment a fair chance.

It seems like a new toenail is growing underneath old one. It's caused by a fungal toenail infection. You may need a topical antifungal medication for treatment. You can ask a pharmacist for appropriate medication. Fugacil cream can also help you. Applying it consistently, my old nail has fallen off and new nail is growing- more quickly than any creams that I've tried.

I too have an overlapping little toenail, following a thickening, months ago, that was surely a fungal infection.

I have been using anti-fungal cream on three fingers for some months and now use it on the toe. The toe seems clear of fungal infection.

For better or worse, I have been filing the upper toenail to reduce its thickness to a slither.