I have hypothyroidism and chronic stress/anxiety. Does low cortisol cause hypothyroidism?

No. Cortisol is made by the adrenal glands whereas hypothyroidism refers to low levels of thyroid hormone from the thyroid gland. Having one does not cause the other. Chronic stress and anxiety also do not cause these disorders. Low cortisol (adrenal insufficiency) is a rare disorder, typically autoimmune related, and must be diagnosed correctly, not simply by a low cortisol level.