Can an oncoming migraine cause a head rush with brief dizziness?

Yes, it can: A migraine is not just simply a headache. It is an attack that is accompanied by various neurological and non-neurological features as well as headache. Migraines headaches are unilateral often starting in the temple or occipital regions; they may even affect the neck and shoulder. Head rush and dizziness could be a symptoms. Re. See a headache or orofacial pain specialist.