Unfortunately, the availability of appointments will depend on the surgeon themselves.
You can ask if that neurosurgeon works with partners in the practice, and if they would have an earlier available appointment.
There is frequently multiple neurosurgeons in one area, and so making an appointment with another one in the area would probably be helpful.
In general, the availability of appointments will vary, from one week to a few months between surgeons, and so I would look at another surgeon to get seen more quickly. You may also want to discuss with your pain managment doctor about something stronger for pain, such as oxycodone (Percocet), as that may help better than the vicodin.