Definitely a big time iron (ferritin) deficiency. Should be around 80. Iron deficiency alone can cause thyroid dysfunction. If a doctor told you it was just "a little low," then get another doctor and fast. Try to find a doctor of functional medicine who knows about the relationship between nutrients and their vital importance thyroid function and conversion.
"Does the thyroid need iron to function? Absolutely, but inorganic forms of iron aren't the way to go. Far superior would be whole foods containing heme iron. Additionally, multiple nutrients are required for healthy thyroid function. Most notably: Vitamin A, zinc, selenium, Vitamin D, iodine. Deficiencies of any of these could negatively affect thyroid health."
As far as your blood tests, the TSH is meaningless without using it in conjunction with both readings from Free T3 and Free T4. I see no Free T3 readings. Without Free T3, the TSH makes it appear all is fine. But we know that's not the case because your ferritin is rock bottom. Rock bottom! Your doctor should know this... but wasn't taught a thing about it. Sad, as you cannot have adequate thyroid function without optimal ferritin levels (among other nutrients).
"For normal thyroid hormone transport and receptor response, you require normal levels of vitamin D and ferritin along with normal levels of cortisol, according to “The Hormone Makeover,” by Donna White. Optimal vitamin D level is 60 to 80 nanograms per milliliter, or ng/mL. The level considered sufficient is 50 ng/mL. Optimal ferritin levels are 90 to 110 ng/mL. The normal range for ferritin is 12 to 300 ng/mL for men and 12 to 150 ng/mL for women."
The TSH drops merely because you are taking thyroid hormone supplements -- not because your thyroid function is necessarily good. Conventional doctors make this same mistake over and over again and patients get sicker because of it. Find yourself a doctor who understands how the body works. Most conventional doctors are clueless in this regard. In the meantime, work on getting your iron levels up.
Your Free T4 is topped out and that is an indication that you're not converting it into the active thyroid homone T3. It is the thyroid hormone T3 that regulates your heart beat, metabolism, body temperature, etc., and is essential to be in all the cells of your body. When T3 is lacking in supply and subsequently in limited levels throughout the body and cells... the entire body can begin to dysfunction.
Correcting all nutrient deficiencies, with priority to those that are essential to thyroid function. There has to be a reason why you are so deficient in iron (and no doubt other nutrients). Could be you lack adequate stomach acid to absorb nutrients from foods and supplements.
It is becoming more and more apparent that many are iodine deficient and that served as the beginning of their hypothyroidism; but being ferritin/iron deficient will do the same. It will allow the thyroid's total functions not to complete their tasks. When you interrupt conversion of inactive T4 to active thyroid hormone T3, you essentially begin a journey down a path of dysfunction throughout the body until it is corrected. That means all facets of what is causing the interruption of T3 into the cells. (Low ferritin, low iodine (always to be taken with selenium), low Vitamin D, low Vitamin A (dry-A, Retinol), Zinc (take with copper), and Selenium). Those are the most essential. For your well-being in the meantime, your B-12 levels should also be checked and corrected.
Hope this helps!