Hypertensive Emergency: This condition is characterized by severely high blood pressure that can cause end-organ damage. The symptoms of perioral numbness and hand numbness could be related to the high blood pressure affecting blood flow and nerve function. Hypertensive emergencies can lead to more severe complications if not promptly addressed.

Hypocalcemia: Low calcium levels can cause numbness and tingling sensations in the hands and around the mouth. Although high blood pressure is not a direct symptom, hypocalcemia can be associated with various conditions that may also affect blood pressure.
Vitamin B12 Deficiency: A deficiency in vitamin B12 can lead to neurological symptoms, including numbness in the hands and feet. While not directly related to high blood pressure, vitamin B12 deficiency can have widespread effects on the body.
Anxiety or Panic Disorder: These conditions can cause physical symptoms such as numbness or tingling sensations, especially in the hands and around the mouth, and can also be associated with elevated blood pressure readings due to stress.

Stroke or Transient Ischemic Attack (TIA): Although the symptoms described do not classically present as a stroke (e.g., facial drooping, arm weakness, speech difficulties), atypical presentations can occur, especially in the context of high blood pressure. It's crucial to consider stroke or TIA due to the potential for severe and irreversible damage if not promptly treated.
Multiple Sclerosis: This autoimmune disease can cause a wide range of neurological symptoms, including numbness. While high blood pressure is not a direct symptom, multiple sclerosis can have varied presentations, making it a "do not miss" diagnosis due to its significant impact on quality of life and the importance of early treatment.

Peripheral Artery Disease (PAD): While PAD typically presents with leg symptoms due to atherosclerosis, in rare cases, it could potentially cause symptoms in the hands, especially if there's significant vascular disease. The perioral numbness would be less directly related but could be part of a broader vascular disease picture.
Sarcoidosis: This autoimmune disease can affect various parts of the body, including the nervous system, and could potentially cause numbness. High blood pressure could be related to kidney involvement or as a separate condition. Sarcoidosis is rare and would be considered if other diagnoses are ruled out and there are additional suggestive symptoms or findings.