High TSH (7.12) accompanied by low cortisol (1.0). T4 and T3 (liothyronine) normal. What causes this? Mom had thyroid cancer. What tests should be done?

You need work-up. You should ask to be seen by an Endocrinolosit. Your question suggests that you may have low adrenal/thyroid function. Multiple gland "failure" is seen in a number of conditions. Certain blood/urine testing is indicated! Good luck! Hope this helps Dr Z.