If the toe is black, that portion is probably necrotic & would most likely need to be removed & a stitch taken by your veterinarian.....if you're talking about just the nail, the blackness is probably where the capillary/blood vessel that feeds the nail has been terminated/torn out and only a small bit of tissue is still holding the nail and will likely drop off, but, depending on how much tissue is still holding the nail, when it does come off or Emmy tears it off, there might be a couple of drops of blood loss.....
If you're asking whether Emmy needs to go to her vet, that's only a decision you can make, you're there & can see how Emmy's treating/holding her foot.....you might want to look at it as you having cut yourself & there was a piece of skin left, that you pressed back down & bandaged, hopping it would it would re-attach, but it dried up & you finally pulled the piece of skin off...it probably hurt & may have caused a drop of blood.....you're the one who would have needed to make the decision to go for medical treatment or take care of it yourself,,,,,I keep a tube of Neosporin cream onhand for small cuts or nail pulls.....
Good luck.....
Neosporin cream because it is not petroleum based as is their ointment.....