The proverbial chicken-egg question. I don't know enough about migraines to reply knowledgeably, but anxiety is a fear response, and they are generally learned. Loud noises, for example, will startle an infant and perhaps generate fear as a primal response, but most fear learning is taken on by watching others behave a certain way in certain circumstances, or by simple classical conditioning, such as when salivating over what we know is going to be savoury and appealing when we put it into our mouths., and later when we only smell the same stimulus.

So, I think your neurologist sounds correct. You may develop anxiety because you 'know what's coming', but you may also have a ruminating reflex where your mind works on, chews, turns over, the same problems (real or imagined) and then generates anxiety. You lose sleep or just being content and feeling secure ruminating over and over again, and eventually your agitated state brings on the dreaded problem you were fearing; a migraine.