I would definitely remove the rest of the detached part of the nail to hopefully prevent a fungus buildup. The most effective and cheapest way to treat toenail fungus is good old 3% hydrogen peroxide. No side effects and extremely effective. Glad to hear you don't have any fungus. The nail will grow back. It will take some time, several months. I have knocked toenails off before and just reading about your mishap made my eyes water remembering the pain. Good luck!