Microvascular Cranial Nerve Palsy (e.g., Diabetic Third Cranial Nerve Palsy): Given the patient's history of diabetes (DM) and the sudden onset of diplopia mainly on lateral gaze, this diagnosis is highly plausible. The pain associated with the diplopia also fits, as these palsies can be painful.

Cluster Headache: The headache and pain radiating to the right eye could suggest a cluster headache, especially if the pain is severe and unilateral. However, the primary symptom of diplopia, particularly on lateral gaze, is not typically a hallmark of cluster headaches.
Migraine with Ocular Symptoms: Some migraines can cause transient visual disturbances, including diplopia, and are often accompanied by headache. The lateral gaze diplopia could be related to a migraine affecting the ocular motor nerves.
Hypertension-related Cranial Nerve Palsy: Given the patient's history of hypertension (HPT), a hypertensive crisis could potentially cause a cranial nerve palsy, leading to diplopia.

Aneurysm or Arteriovenous Malformation (AVM): Although less likely, an aneurysm or AVM pressing on the third cranial nerve could cause diplopia, especially if it involves the posterior communicating artery. The presence of pain and the acute onset of symptoms make this a critical diagnosis not to miss due to its potentially catastrophic consequences if ruptured.
Giant Cell Arteritis: This condition can cause visual disturbances, including diplopia, and is accompanied by headache. It's a diagnosis that should not be missed due to the risk of vision loss if not promptly treated.
Stroke or Transient Ischemic Attack (TIA): While the patient does not exhibit typical stroke symptoms like body weakness or slurred speech, a stroke or TIA in certain brainstem locations could cause isolated cranial nerve palsies leading to diplopia.

Multiple Sclerosis: An episode of diplopia could be a presenting symptom of multiple sclerosis, especially if there are other neurological symptoms or signs. However, the absence of other neurological deficits and the patient's demographic characteristics make this less likely.
Myasthenia Gravis: This autoimmune disorder can cause fluctuating muscle weakness, including eye muscles, leading to diplopia. It's rare and would typically present with more widespread or fluctuating symptoms.
Tolosa-Hunt Syndrome: A rare condition characterized by painful ophthalmoplegia (paralysis of the eye muscles), which could cause diplopia. It's due to nonspecific inflammation of the cavernous sinus or superior orbital fissure.