Migraine with Aura: This condition is characterized by neurological symptoms, including visual auras, sensory changes, and sometimes olfactory hallucinations (phantom smells), accompanied by headaches. The sharp pain in the back of the head could be part of the migraine headache, which often presents with unilateral, throbbing pain but can also occur bilaterally or in the back of the head.

Tension-Type Headache: While less likely to cause phantom smells, severe tension-type headaches can lead to sharp pains in the back of the head and, in some cases, may be accompanied by sensory disturbances due to muscle tension and stress.
Occipital Neuralgia: This condition involves inflammation of the occipital nerves and can cause sharp, stabbing pains in the back of the head. While it doesn't typically cause phantom smells, the pain can be severe enough to trigger other sensory disturbances.
Sinusitis: Inflammation of the sinuses can lead to changes in smell perception, including phantom smells, and can cause headaches, including sharp pains in the back of the head if the occipital sinuses are involved.

Subarachnoid Hemorrhage: Although rare, a sudden, severe headache (often described as "the worst headache of my life") can be accompanied by neurological symptoms, including sensory disturbances. The sharp pain in the back of the head could be indicative of a hemorrhage, especially if it's sudden and severe.
Meningitis: Inflammation of the meninges can cause severe headaches, fever, and neurological symptoms, including changes in sensory perception. While phantom smells are not a common presenting symptom, the combination of sharp head pain and any neurological deficits warrants consideration of this diagnosis.
Temporal Arteritis: This condition, which involves inflammation of the blood vessels in the head, can cause headaches, visual disturbances, and occasionally changes in smell. It's a critical diagnosis to consider due to the risk of blindness if not treated promptly.

Epilepsy (with Olfactory Seizures): In some cases, seizures can manifest with olfactory hallucinations (phantom smells) and could potentially be accompanied by sharp pains in the back of the head, especially if the seizure activity involves parts of the brain that process pain.
Schizophrenia or Other Psychotic Disorders: While not primarily neurological in nature, these conditions can involve hallucinations, including olfactory hallucinations. However, the presence of sharp pain in the back of the head would be unusual as a primary symptom.
Brain Tumors: Tumors in certain areas of the brain could potentially cause both phantom smells (if they affect areas involved in olfaction) and sharp pains in the back of the head (if they cause increased intracranial pressure or involve pain-processing areas).