Autonomic Dysfunction: Given the patient's history of Postural Orthostatic Tachycardia Syndrome (POTS) and symptoms such as headaches, numbness in hands, back pain, neck pain, fatigue, and feelings of near syncope, autonomic dysfunction is a plausible explanation. These symptoms can be exacerbated by hormonal changes, which might explain the improvement with birth control.

Migraines: The patient's headaches and eye pressure could be indicative of migraines, which are often accompanied by neurological symptoms like numbness and can be influenced by hormonal changes.
Fibromyalgia: This condition is characterized by widespread musculoskeletal pain, fatigue, and sleep, memory, and mood issues, which align with some of the patient's symptoms.
Anxiety/Depression: The patient's history and current symptoms could also suggest an underlying mental health condition, which is common in individuals with chronic illnesses and could exacerbate physical symptoms.
Hormonal Imbalance: Despite being on birth control, which has helped some symptoms, there could still be an underlying hormonal imbalance contributing to her symptoms, especially considering her history of thyroid cancer and potential for thyroid hormone imbalances.

Thyroid Storm: Although less likely, given her history of thyroid cancer, a thyroid storm is a life-threatening condition that requires immediate attention. Symptoms can include headaches, fatigue, and eye pressure, among others.
Multiple Sclerosis (MS): The numbness, particularly on one side, and other neurological symptoms could suggest MS, a condition that would have significant implications for her health and requires prompt diagnosis.
Spinal Cord Compression: Back and neck pain, along with numbness, could indicate spinal cord compression, which is a medical emergency.
Pituitary Adenoma: Given her symptoms and history, a pituitary adenoma could be a possibility, especially if there's a hormonal imbalance or if the thyroid cancer has metastasized.

Ehlers-Danlos Syndrome: This genetic disorder can cause symptoms similar to what the patient is experiencing, including joint pain, fatigue, and autonomic dysfunction.
Mitochondrial Myopathies: These are a group of disorders that affect the mitochondria and can cause a wide range of symptoms, including muscle pain, fatigue, and neurological issues.
Adrenal Insufficiency: Although rare, this condition could explain some of the patient's symptoms, especially if there's an issue with her adrenal glands following her thyroid cancer treatment.