I am also hypothyroid and a site called stopthethyroidmadness.com helped me realize I might have adrenal concerns even if the blood test said I was fine.
I found a doctor who would give me a urine test for adrenals and sure enough there was a deficiency. While I was waiting I took Isocort, available on the web, but now take Hydrocortisone. You don't usually have to take them forever, just until your adrenals heal.