your fingernails protect your fingers and when you broke the nail down so far you exposed skin that hasn't been exposed previously. so yes you have probably "hit" a nerve but you hit nerves any time you bump yourself. what you're feeling is nerve endings that are more sensitive due to this unexpected exposure. it will go away in time. keep the area protected from further injury.
i broke my pinky fingernail down to the skin and have been feeling a tingling/slight numbness. did i hit a nerve?