There are plenty of tests which can show what's wrong with you - but they're not "standard" in the sense of doctors using them.
If your morning cortisol is above a certain level or below a certain level; if your morning, before-you-get-out-bed axillary body temperature is above or below a certain temperature (under 97.8 or above 98.6); if your blood pressure deviates by a certain amount over a 16-hour day; if your average temps deviate by more than 0.2 F from day to day; if you have post-exertional malaise… you have an HPA malfunction of one kind or another.
I'd say "you should also get your thyroid checked" but the blood tests for that are atrociously useless. Check the symptoms. Low body temp, especially in the morning before you get out of bed (mine ranges from 96.5-97.4), slow heart rate if you're not an athlete (mine is 50-60 bpm and I am NOT an athlete!), puffy face/eyes, myxedema (non pitting) swelling/thickened rubbery skin on your upper outer arm or shin, changed ankle-tap reflexes, very cold extremities, Raynaud's phenomenon, etc., those are the signs that are actually diagnostic of a thyroid insufficiency.
These are how doctors have diagnosed and treated low thyroid successfully for a hundred years. The blood tests are a new thing but they aren't very indicative of actual dysfunction (or function).
All of the above is like a lot like low blood pressure. Low blood pressure is only defined by numbers when it becomes dangerous to life. Otherwise, you're diagnosed with low blood pressure if your blood pressure is "normal" or below and you have symptoms. E.g. I have low blood pressure at 100-110/60-70 even though that's considered just fine, because I feel faint when I stand up and other symptoms.
Generally, the best resource I've found is _From Fatigued to Fantastic_. It helped me get much, much, better.