Your concern about your problem is understandable. relax and think over the following points for some time.
are two different conditions. The first thing you have to consider is whether your diagnosis has been done by a specialist in handling anxiety/migraine. Anxiety itself can cause headaches
which can be quite distressing.
Irrespective of whether it is anxiety or migraine (although they cannot be "cured" permanently) your problem can be effectively controlled with available allopathic medicines. Expecting a magical cure for such conditions would be unrealistic and do not fall prey to such claims. If it can be cured, then it is neither anxiety nor migraine.
Consult a psychiatrist
for detailed evaluation so that a proper diagnosis can be made and treatment planned accordingly. All the best.