What tests and specialists should I pursue for months of migraine with aura?

[Jerry.W]

I've been experiencing what I think are migraine symptoms for the past several months, but my doctor's initial assessment was inconclusive. The episodes start with a visual aura—flashing lights and blind spots in my peripheral vision—followed by intense, throbbing pain on one side of my head, nausea, and sensitivity to light and sound. Over-the-counter painkillers do almost nothing. For others who have been diagnosed, does this sound typical, and what specific tests or specialists should I push for to get a definitive diagnosis? How do you differentiate between migraines and other types of severe headaches, and what lifestyle or dietary triggers should I start tracking in a diary?