How long is the recovery period for a dry socket?

Go see your dentist. You dont have to suffer with dry socket. If you go see your dentist, dry socket paste will provide almost instant relief. (wont taste great) but will make it all better.
Several days to 10. A dry socket is normally failure for the wound to initially heal over properly. There may be uncovered exposed bone. Normally your dentist can pack the socket with medication, changing it every day or so for 2-3 day but sometimes it can take longer.