I hit my big toe and half of the nail turned black. i peeled it off because it was hurting me. what do i do?

Treat as wound: Treat the open wound as you would a cut with neosporin and cover to protect it. Then wait for the toenail to slowly grow back out.

Usually nothing: If it is no longer hurting you, no longer bleeding or oozing. Do nothing. Time will do the rest. If it looks infected still tender, bleeding, there is pus have it checked asap.

Nothing: You treated it already. A new nail will grow back don't worry. That was blood (the black color). You don;t have to cover it unless there is redness then you may want to apply a topical antibiotic and cover it with a band-aid.