How do you distinguish the difference between adrenal fatigue, hypothyroidism, and perimenopause by symptoms alone? They all have the same symptoms.

Medical evaluation. While symptoms may overlap, untreated hypithyroid and adrenal insufficiency (not aware of the term adrenal fatigue) are potentially life threatening with adrenal complaints including weight loss, abdominal pain, nausea, vomiting, weakness and thyroid complaints including weight gain, fatigue, constipation, cold intolerance. Your physician can evaluate for the cause of your symptoms.
Difficult. Adrenal fatigue and hypothyroidism often coexist. Do labs to find out. Check free T3 and reverse t3. Ft3 should be in upper range and rt3 in lower range. If your ratio is off, you may need Armour Thyroid or t3, and synthroid (thyroxine) would be the wrong med for you. 24 hour urine hormones can give us a picture of adrenals. Or do 24 hour salivary cortisol.