Migraine: This is the most likely diagnosis given the location of the pain (left temple) and the radiation of pain to the back of the eye, which are common features of migraines. Migraines are also more prevalent in females.

Cluster Headache: Although less common than migraines, cluster headaches can cause severe, unilateral pain often described as occurring around the eye and can radiate to the temple area. They are more common in women during certain times of the year.
Tension Headache: While typically bilateral, tension headaches can occasionally present unilaterally and may cause pain that feels like it's behind the eye due to the referral of pain from the scalp and neck muscles.
Temporal Arteritis (Giant Cell Arteritis): Although more common in older adults, temporal arteritis can cause unilateral headache, often described as a sharp pain, and can be associated with visual symptoms due to involvement of the ophthalmic artery.

Acute Angle-Closure Glaucoma: A medical emergency that can cause severe eye pain, often described as a sharp pain in or around the eye, and can be accompanied by headache, nausea, and vomiting. It's crucial to diagnose promptly to prevent permanent vision loss.
Cavernous Sinus Thrombosis: A rare but potentially life-threatening condition that can cause headache, eye pain, and visual disturbances due to thrombosis of the cavernous sinus. It often presents with additional symptoms such as fever and cranial nerve palsies.
Stroke or Transient Ischemic Attack (TIA): While less common, stroke or TIA can present with sudden onset of headache and eye pain, among other neurological symptoms. It's critical to consider and rule out these conditions due to their high morbidity and mortality.

Trigeminal Neuralgia: A condition characterized by sudden, severe, shock-like pain around the eyes, lips, or nose mainly because of abnormal blood vessels pressing on the trigeminal nerve in the head. It's less likely given the description but should be considered if other diagnoses are ruled out.
Idiopathic Intracranial Hypertension (IIH): Also known as pseudotumor cerebri, IIH can cause headache and visual disturbances, including transient visual obscurations and double vision. It's more common in obese women of childbearing age but is less likely given the specific pain pattern described.
Ophthalmic Herpes Zoster: Shingles involving the ophthalmic division of the trigeminal nerve can cause severe pain in the eye and forehead, which may precede a rash. It's less common and typically presents with a distinct rash, but the pain can be a preceding symptom.