Poor Zoe. My bridge boy, Keno, did that twice -- he was a wild thing in his younger days. The second time he did it was very bloody and painful. Anyway, my vet told me to keep it very clean to prevent a nail bed infection. I kept a cotton baby sock taped over it to keep him from licking it (he was terrible about that) and then put plastic wrap over it when he went outside to keep the mud/dirt from getting to it.
Keno was on oral antibiotics and he gave me something to clean it with, but I don't remember what it was. I now use a natural ointment called Wounded Warrior for most cuts and wounds. It doesn't sting and it's very soothing (has calendula in it). I use it on myself too.
Feel better soon Zoe.