The 26th is not so far off.
If you're paying out of pocket for all the testing, it will get expensive, so you might have to make some choices. If it comes down to choosing between the micronutrients and inflammation or gut infections, I'd test adrenal function and for the gut infections and inflammation. You can take most of the vitamins/minerals safely, even if you aren't deficient and excess will be excreted in waste, but if you have a gut infection, it can go on for years without you knowing it and only gets worse over time.
Of course, this excludes the major nutrients, such as iron, B-12, vitamin D, Folate, etc.
If you're already supplementing with 5000 IU vitamin D, the doctor may choose not to go with a mega dose; he may just see what the 5000 IU does over a period of time. Iron is best supplemented under a doctor's supervision.
Yes, I suspected that's where you came up with your list of symptoms; unfortunately, the list in the link is somewhat misleading, because if you note the author has lumped "Related Autoimmune or Endocrine Diseases" and "Other Related Conditions" into the symptoms list for hypothyroidism. They aren't really "symptoms" of hypothyroidism - the relationship with other autoimmues is that once a person has one autoimmune, the chances of getting another are greater than if they didn't have any autoimmunes.
Your Reverse T3 (rT3) is high in the range, but we don't go by the actual result; it's a ratio between Free T3 and rT3 from the same blood draw. Ideally, that ratio should be above 2 and I calculated yours at 10.2.
Please accept my apology if I sound like I think you don't have hypothyroidism, because that's not the case... I "do" think you're hypo, due to your low Free T3 and a possible conversion issue; however, I also think you have other things going on, as well, as indicated by the low vitamin D and ferritin.
Low Vitamin D can cause some of the symptoms you've listed, so once you begin supplementing and bring your levels up, some symptoms may begin to subside. Sometimes, doctors prescribe "mega-doses" of vitamin D, which are, typically, 50,000 IU/week for a short period to raise levels more quickly - did your doctor do that or just suggest that you begin an OTC supplement? What dose was suggested?
With your low ferritin level it would be good if you could get a complete iron panel before you start supplementing to see what your baseline is.
I agree that the functional medicine doctor will probably want to order more tests. One that I would highly recommend is Folate, which goes hand in hand with B-12 and even though your B-12 is excellent, your Folate could be low, causing some symptoms of B-12 deficiency. Another I would suggest is hs-C-reactive protein, which measures inflammation in the body.
Another test I might recommend is a micronutrient test, as there are some vitamin/mineral deficiencies that can cause unpleasant symptoms that we don't, often, think about. The problem is that these panels can get very expensive and most insurance doesn't cover them.
When something happens and one doesn't have optimal thyroid hormones, the adrenal glands tend to kick in to help take up the slack. For this reason, due to your symptoms, adrenal testing would probably, also be in order and it's good that you're going to a functional medicine doctor, as they're more inclined to do that testing than conventional doctors are.
How long before your appointment with the functional medicine doctor?
Can you, please, post your actual ferritin, vitamin D and B-12 results, with reference ranges?
Some of the symptoms you listed aren't really those of hypothyroidism, but they could be stand alone conditions or symptoms of other underlying conditions. Have you had tests done to determine whether you have any other conditions?
It would be helpful to know what hypo symptoms you have.
Your TSH doesn't indicate hypo, nor does your Free T4, which is higher than the mid range level we, typically, recommend to be optimal. Your Total T4 is actually over the reference range, which indicates that your thyroid is working; however, your T3 is in the lower half of its range, indicating that possibly you aren't converting the T4 to T3 as you should be and since Free T3 is the hormone that's used by every cell in body, this could explain your hypo symptoms.
Your antibody tests indicate that you don't have Hashimoto's since the results are, both, less than the reference ranges. I'd still recommend that you ask for a thyroid ultrasound, as some people have been diagnosed with Hashimoto's on the basis of characteristics of their thyroid gland as seen on ultrasound, even if antibody results were negative, as yours are. It would also be helpful to know if you have nodules on your thyroid gland. While nodules nodules are, typically, harmless, it's still good to know if they're present or not and keep watch on them.
This would all bring me to wonder if you've had ferritin and some other vitamins/minerals tested. Ferritin is the iron storage hormone and iron is necessary for the conversion of theT4 storage hormone to the usable T3 hormone. Vitamin B-12, vitamin D and magnesium deficiencies can cause many hypo-like symptoms.
Selenium has also been shown to aid in the conversion of T4 to T3.
If I were the functional medicine doctor, I would probably want to do more blood tests to make sure vitamin/mineral deficiencies weren't contributing to your problems.