What kind of doctors treat a carotid cavernous fistula?

Neurosurgeon: This is a direct connection between the carotid artery and the low pressure venous system in the cavernous sinus. It can cause significant dysfunction of cranial nerves, cause swelling of veins in the upper face and eye surface, and is in fact very dangerous and requires immediate attention from a neurosurgeon to prevent permanent damage or even death.

Most are: Treated by neurointerventional radiologists. See snisonline.Org.