Vestibular Neuritis or Labyrinthitis: This condition is characterized by inflammation of the vestibular nerve or labyrinth, leading to nystagmus with the fast phase away from the affected side. Given the presentation of horizontal unilateral nystagmus with the fast phase to the left, it suggests a left-sided vestibular issue, making vestibular neuritis or labyrinthitis a plausible diagnosis.

Benign Paroxysmal Positional Vertigo (BPPV): Although BPPV typically presents with rotational vertigo and nystagmus, it can occasionally cause horizontal nystagmus. The diagnosis is based on the history of vertigo triggered by specific head movements and the presence of nystagmus during the Dix-Hallpike maneuver.
Meniere's Disease: This inner ear disorder can cause episodes of vertigo, hearing loss, tinnitus, and aural fullness. Nystagmus may be observed during acute attacks, with the fast phase typically beating away from the affected ear.
Vestibular Migraine: Some patients with migraines can experience vertigo and nystagmus, which can be unilateral. The nystagmus can be horizontal and may have a fast phase to one side, although it is often more variable than in vestibular disorders.

Posterior Circulation Stroke: A stroke in the posterior circulation, including the brainstem or cerebellum, can cause nystagmus. It is crucial to consider this diagnosis, especially if accompanied by other neurological deficits, as timely intervention is critical.
Multiple Sclerosis: Demyelinating lesions in the brainstem or cerebellum can lead to nystagmus. Given the potential for significant morbidity if not treated, multiple sclerosis should be considered, especially in younger patients or those with a history suggestive of demyelinating disease.
Acoustic Neuroma: A tumor on the vestibulocochlear nerve can cause unilateral nystagmus, among other symptoms like hearing loss and tinnitus. Early diagnosis is important for treatment planning.

Congenital Nystagmus: Although typically diagnosed in childhood, some forms of congenital nystagmus can present later in life. It often has a horizontal component but is usually bilateral.
Periodic Alternating Nystagmus: A rare condition characterized by nystagmus that changes direction over time, often associated with central nervous system disorders.
Medullary Thyroid Cancer with Brainstem Metastasis: Extremely rare, but in cases of known medullary thyroid cancer, metastasis to the brainstem could potentially cause nystagmus among other neurological symptoms.