Final answer:
Cluster headaches are a likely diagnosis for this woman's symptoms of throbbing headaches behind one eye that worsen over time.
Step-by-step explanation:
This woman's presentation of throbbing headaches behind one eye that worsen over time is consistent with cluster headaches. Cluster headaches are characterized by severe unilateral pain that occurs in bouts or clusters, usually around one eye. They tend to be throbbing or pulsating and can be accompanied by other symptoms such as eye redness, tearing, and nasal congestion.