A conventional doctor will not be able to diagnose you with adrenal fatigue. Unless they are extremely liberal in their practices they will probably think you are crazy for even mentioning it. The only thing they can diagnose you with is called Addisons disease and that is basically when your cortisol has completely crashed and your adrenals arent working anymore.
I dont want to get into all the specifics but adrenal fatigue doesnt fit into an ICD code so therefore doctors will not recognize it. There is no magic drug that will help with adrenal fatigue so therefore there is no profit to be made in treating it. I suggest you go to a naturopath who can run a saliva cortisol test. These are more accurate than blood tests and insurance will cover them.
The thyroid is a different story. There are blood tests they can run to determine if your thyroid is low and they can start you on thyroid replacement hormone.
I would also suggest you stop working out so much. If you do have adrenal and thyroid problems then strenous exercise is the last thing you should be doing. I have both adrenal fatigue and low thyroid and the extent of my exercise is a daily walk and some yoga. I know exercise makes you feel better temporarily but in the long run it will further deplete your energy and adrenals.
Also make sure you are eating enough. If you arent already I would start tracking your daily calories. If you exercising and not eating enough to offset the exercise then you are further depleting your body.
Vitamin C and Ashwagandha are usually good for adrenals and if your adrenals are low you can also try adrenal extracts.