Cluster Headache: This condition is characterized by severe, unilateral headaches often accompanied by autonomic symptoms such as facial flushing, lacrimation, and nasal congestion. The pain can sometimes radiate to the arm, and blurred vision can occur due to the intense pain or associated autonomic features.

Migraine with Aura: Migraines can cause unilateral pain, and some individuals experience aura symptoms, including visual disturbances that could be described as blurred vision. Facial flushing can also occur.
Temporomandibular Joint (TMJ) Disorder: TMJ disorders can cause unilateral facial pain and might lead to referred pain in the arm. Blurred vision could be related to tension or pain affecting the muscles around the eyes.
Cervicogenic Headache: These headaches originate from the cervical spine and can cause unilateral pain, sometimes accompanied by arm pain due to referred pain patterns. Facial flushing and blurred vision could be secondary to pain and tension.

Stroke or Transient Ischemic Attack (TIA): Although less likely, it's crucial to consider stroke or TIA, especially if the symptoms are sudden in onset. Facial weakness, arm weakness, and visual disturbances can be symptoms of a stroke.
Multiple Sclerosis: This condition can cause a wide range of neurological symptoms, including vision problems, pain, and autonomic dysfunction. While less common, it's a diagnosis that should not be missed due to its significant implications.
Giant Cell Arteritis: This condition can cause headaches, visual disturbances (including blurred vision), and facial pain. It's a medical emergency if vision loss is threatened.

Raeder's Syndrome: A rare condition characterized by unilateral facial pain, ptosis (drooping eyelid), and miosis (constricted pupil) on the same side, which could potentially cause blurred vision. It's a rare diagnosis but should be considered in the differential.
Harlequin Syndrome: This is a rare condition that affects the autonomic nervous system, causing unilateral facial flushing and sweating. While it doesn't typically cause pain or blurred vision directly, it could be considered in a broad differential for unusual autonomic symptoms.
Pancoast Tumor: A type of lung cancer that can cause shoulder and arm pain due to invasion of the brachial plexus, along with Horner's syndrome (which could cause blurred vision due to ptosis or miosis). Facial flushing is less common but could occur due to autonomic dysfunction.