Yes, you need to see a neurologist who is a migraine - headache specialist. Not all neurologists are.
Forget the other specialties you have seen. And as a long time migraine sufferer (beginning with a concussion) I can tell you it is very common to go 'round and 'round the migraine medication cycle. Very common initially for a new migraine medication to be so helpful and suddenly, without warning, ceases to be so. So it's on to the next recommended medication. You need a "preventative" medication in addition to an "abortive" medication.
Plus a migraine "arsenal"...migraine ice caps, eye shields, sunglasses for TV/computer glare, medication for nausea & medication for dizziness. Even herbal teas - ginger/peppermint are good. I have found a neuro-modulating device can be helpful, check them out on line. Only one you can get without a prescription from your physician. Found out what are your migraine "triggers", mine is anxiety and stress (big time) - and skipping a meal. I also have chronic insomnia which does not help but so sensitive to sleeping aids I take nothing for sleep. And get peppermint aromatherapy. It can come in a small "roll on" tube, apply to skin/under your nose...peppermint does help migraines (at least for me). More migraine medications have been approved by the FDA in the last 5 years vs. the last 20 years. And there are also the "off-label" medications which can help migraine sufferers.
Finally check out the World Migraine Summit held annually or the National Headache Foundation for more resources. Most people do not know that "migraine" is NOT a headache but a neurological disorder. It can be a real monster, beyond debilitating. I wouldn't wish it on my worst enemy if I had one. All my very best to you!