Benign Paroxysmal Positional Vertigo (BPPV): This condition is characterized by brief, intense episodes of vertigo triggered by specific head movements, which could explain the dizziness. However, the shaking of the right arm might be more indicative of another condition. Still, given the prevalence of BPPV and its potential to cause significant dizziness, it's a plausible starting point.

Essential Tremor: A common movement disorder that can cause shaking, especially in the arms. If the shaking is more pronounced in the right arm and is accompanied by dizziness, essential tremor could be a consideration, especially if the dizziness is not as severe or is secondary to the anxiety of dealing with tremors.
Parkinson's Disease: Early stages of Parkinson's can present with unilateral tremors and might also include non-motor symptoms like dizziness. The combination of severe dizziness and shaking, particularly if the shaking is more pronounced at rest, could suggest Parkinson's.
Multiple Sclerosis (MS): MS can cause a wide range of neurological symptoms, including tremors and dizziness, due to lesions in the central nervous system. The symptoms can be highly variable and might include severe dizziness and arm shaking.

Stroke or Transient Ischemic Attack (TIA): Although less likely if the symptoms are chronic, any new onset of severe dizziness combined with shaking of an arm could indicate a stroke or TIA, especially if accompanied by other symptoms like facial drooping, speech difficulties, or weakness. These conditions are medical emergencies.
Brain Tumor: A tumor in the brain could cause a variety of symptoms depending on its location, including dizziness and tremors. While less common, missing a brain tumor could have severe consequences.
Meningitis or Encephalitis: Infections of the meninges or brain can cause severe symptoms, including dizziness and tremors, along with fever, headache, and confusion. These are medical emergencies.

Wilson's Disease: A genetic disorder that leads to copper accumulation in the body, causing neurological symptoms including tremors and balance problems. It's rare but could be considered in young patients with these symptoms.
Spinocerebellar Ataxia: A group of genetic disorders that affect the cerebellum, leading to ataxia (loss of coordination) and could include symptoms of dizziness and arm shaking.
Vestibular Migraine: While migraines are common, vestibular migraines, which can cause severe dizziness, are less so. If accompanied by arm shaking, this could be a rare but possible diagnosis.