What do you suggest i do to get a piece of broken off nail out from my toe?

Carefully: Wash foot with soap and water, apply an antiseptic to area and remove broken nail. If partially attached still, trim what you can. If too painful, see a podiatrist who will numb your toe and remove the nail.

If you have to : Ask, likely better off seeing the foot doctor who can do this in minutes. You may need local anesthesia depending on the appearance of the nail andsurrounding skin.