Congenital Hypothyroidism: This is the most likely diagnosis given the elevated TSH level at 13 days of life. Congenital hypothyroidism is a common condition where the thyroid gland doesn't produce enough thyroid hormone, which is essential for growth and brain development. The elevated TSH level is a key indicator of this condition, as the pituitary gland increases TSH production in an attempt to stimulate the thyroid gland to produce more thyroid hormone.

Transient Hypothyroidism: This condition can cause elevated TSH levels in neonates, often due to maternal thyroid-blocking antibodies or exposure to excessive iodine. It is usually temporary and resolves on its own.
Thyroid Dysgenesis: Although less common, thyroid dysgenesis (abnormal development of the thyroid gland) can also lead to elevated TSH levels. This condition can be part of congenital hypothyroidism but is listed separately as it implies a specific underlying cause.

Pituitary Hypoplasia or Hypopituitarism: Although rare, these conditions can lead to central hypothyroidism, where the pituitary gland does not produce enough TSH, leading to low thyroid hormone levels. However, in some cases, especially with partial defects, TSH levels might be inappropriately normal or slightly elevated, making it crucial not to miss these diagnoses.
Thyroid Hormone Resistance: A condition where the body's tissues are resistant to thyroid hormone, leading to elevated TSH and thyroid hormone levels. It's crucial to diagnose this condition to avoid unnecessary treatment.

Thyroiditis: Inflammation of the thyroid gland can cause transient elevations in TSH levels. While rare in neonates, it's an important consideration, especially if other signs of inflammation are present.
Genetic Disorders Affecting Thyroid Function: Certain genetic disorders can affect thyroid hormone production or regulation, leading to elevated TSH levels. These are rare but important to consider, especially if there's a family history of thyroid disorders or other genetic conditions.