Final answer:
The most appropriate step in managing this patient's frequent migraine attacks is to begin a prophylactic treatment with amitriptyline, given its beneficial effect on reducing migraine frequency and treating coexisting major depression.
Step-by-step explanation:
The patient's clinical presentation is highly suggestive of migraines, given the severe, pulsating headaches with accompanying nausea, vomiting, and unilateral location, and presence in her family history. Additionally, the sumatriptan response indicates that her headaches are indeed migrainous. Considering her case, the most appropriate next step in management would be the initiation of a prophylactic treatment to reduce the frequency and severity of her migraine attacks. Amitriptyline, a tricyclic antidepressant, is commonly used for migraine prophylaxis and has the added benefit of treating her coexisting major depression. Other options such as inhalation of 100% oxygen, CT scan, lumbar puncture, and intranasal dihydroergotamine are not indicated in this scenario as first-line management for frequent migraines with a normal neurological examination and no evidence of papilledema.