Cervical Strain or Whiplash: This is the most likely diagnosis given the history of a fall and subsequent nasal fracture, which suggests significant trauma to the head and neck. The pain in the back of the head is consistent with muscle strain or whiplash injury.

Cervical Facet Joint Pain: The fall could have caused injury to the facet joints in the cervical spine, leading to pain in the back of the head.
Suboccipital Muscle Strain: The muscles at the base of the skull could be strained due to the fall, causing pain in the back of the head.
Post-Traumatic Headache: Headaches are common after head trauma and can be caused by a variety of factors, including muscle tension, stress, and minor injuries to the brain.

Subarachnoid Hemorrhage: Although less likely, a subarachnoid hemorrhage could occur after a fall, especially if there was significant trauma to the head. This condition is life-threatening and requires immediate medical attention.
Cervical Spine Fracture: A fracture in the cervical spine could cause pain in the back of the head and is a potentially life-threatening condition if not promptly diagnosed and treated.
Epidural Hematoma: This is a rare but potentially life-threatening condition where bleeding occurs between the skull and the dura mater, which could be caused by a fall.

Occipital Neuralgia: This condition involves irritation of the occipital nerves and can cause pain in the back of the head, but it is less common and typically not associated with trauma.
Atlantoaxial Subluxation: This is a rare condition where the joint between the atlas (C1) and axis (C2) is disrupted, which could cause pain in the back of the head, but it is less likely without specific symptoms or risk factors.