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Psychogenic Vertigo can produce profound dizziness without having an organic cause. www.dizziness-and-balance.com/disorders/central/unlocalized.htm
Up until the headaches part, a psychological cause is still possible, and even with the headaches, might still be a factor. Are your migraines unilateral or bilateral?
BnotAfraid referred to a particular type of migraine, I had the migraine once, it's known as a Basilar Migraine (If I'm think of the same thing she was).www.achenet.org/resources/basilartype_migraine/
Two of your medications are anti-epileptic drugs. They may, or may not, be effective for migraines. But if your migraines are from vascular constriction, other medications can be used, such as Beta Blockers, sometimes Anti-Depressant medications are used.
Migraines are a vascular event. The aura, symptoms that occur in some as a prelude to the painful migraine, are often caused by vascular constriction, with the dilation (perhaps over dilation) that follows produces the pain associated with migraines.
To prevent the vascular spasms, be sure to eliminate coffee, chocolate, some cold and diet medications, energy drinks, recreational drugs, etc. In addition, get 7 to 8 hours of sleep if possible, but over sleeping has been known to trigger migraines, so avoid sleeping too long.
Be sure to follow up with your doctor and inform him/her of changes in symptoms and any concerns you have.