None in particular. Migraines in general are caused by pressure changes and the contractions of blood vessels in various regions of the brain and associated tissues. Commonly the causes are compounds in the blood, from food, disease, hormones and so on. If they enter one side of the brain rather than another, then the subjective effect is on the other side.

Depending on your personal physiology and the cause of your migraines, it is quite common for the effect to change sides, or to attack both sides on occasion. It has nothing special to do with "left-brain" or "right-brain" in the sense that the two halves differ in their roles (speech versus art and all that), but is more like being slapped on one side of the head or the other.  

Not that that is much compensation; all my sympathy!

Go well,

Jon