First of all Theland, may i congratulate you on a full, accurate and informative account of your symptoms, modern medicine has removed accurate history with either "links" or " modern investigative techniques....well done.
Also I agree with the post of Kvalidir, although not completely typical of Cluster headaches (migrainous neuralgia) I cannot think of a better diagnosis.
Buenchichico's link with cross the Ts and dot the eyes.
I would ask the doctor if he supports that diagnosis and if so would he be prepared to prescribe Imigran for the attacks.