Anxiety or Panic Disorder: This condition is often associated with symptoms such as periorbital sweating and dizziness due to the body's 'fight or flight' response. The physical symptoms can be triggered by anxiety or panic attacks, making it a common and likely diagnosis for these symptoms.

Hypoglycemia: Low blood sugar can cause sweating, dizziness, and shakiness. Periorbital sweating could be part of a broader autonomic response to hypoglycemia.
Migraine: Some migraine attacks can include autonomic symptoms like sweating (which could be localized, including periorbital areas) and dizziness or vertigo.
Hyperthyroidism: This condition can lead to increased sweating, heat intolerance, and tremors, along with potential dizziness due to palpitations or other cardiovascular effects.

Myocardial Infarction or Cardiac Ischemia: Although less common, cardiac issues can present with atypical symptoms, including sweating and dizziness, especially in women or diabetic patients. Missing this diagnosis could be fatal.
Pheochromocytoma: A rare tumor of the adrenal gland that can cause episodic hypertension, sweating, palpitations, and dizziness due to excessive catecholamine release.
Stroke or Transient Ischemic Attack (TIA): While typically presenting with more focal neurological deficits, some strokes or TIAs can cause dizziness and sweating, especially if the brainstem or cerebellum is involved.

Autonomic Dysfunction: Conditions affecting the autonomic nervous system, such as dysautonomia, can lead to a variety of symptoms including abnormal sweating patterns and dizziness.
Neurological Disorders: Certain rare neurological conditions, like multiple system atrophy, can affect autonomic function, leading to symptoms like periorbital sweating and dizziness.
Medication Side Effects: Some medications can cause sweating and dizziness as side effects, though this would typically be identified through a thorough medication history.