I have something similar, a big toe nail hanging by a thread which I have been keeping a plaster on to stop me catching it.
It did seem to be infected so saw the GP and had antibiotics and a referral to a podiatrist, the wait has been 10 weeks, I see them in a couple of weeks, I suppose it may come off in the meantime.
Somebody I know said it happened to her and a new one had just grown underneath.
I was not sure what to do which is why I went to the GP.