When I do the retesting in 6 weeks, they ordered the Free T3 and Free T4 tests :)
Red_Star gave you good info on ferritin.
I noted that you said you were going to be tested for T4 and T3. If you ask for T4 and T3 you will likely get Total T4 and Total T3. Make sure you always ask for and get Free T4 and Free T3. Those are the biologically active thyroid hormones.
Excerpt from Tired Thyroid - Thyroid Hormone Requires Iron, Cortisol, Selenium, Iodine...
"Low iron, or more specifically, low ferritin, is one of the most overlooked causes of low thyroid function. [1] Ferritin is the stored form of iron that is used by the cells and a better measure of available iron levels than serum iron. Iron is a component of multiple enzymes involved with cellular metabolism, so low iron means poorly functioning enzymes, and less than optimal metabolism. Those with low iron also have low T4 and even lower T3 levels. [12] Iron deficiency also lowers thyroid peroxidase (TPO) activity. TPO is an iron-containing enzyme that initiates the first two steps in thyroid hormone synthesis. [2]
Low ferritin can cause negative reactions like palpitations, nervousness, and anxiety in someone starting thyroid hormone replacement. Someone described it like being shot out of a cannon. It is therefore imperative that ferritin not be at the bottom of the range before starting thyroid hormone medication. [3] The following are just a few reasons why someone’s ferritin could be low:
poor gut absorption of iron from celiac disease (another autoimmune disease)
the use of antacids (acid is necessary to digest foods) [4]
poor gut absorption from low digestive acids/enzymes due to hypothyroidism [5]
not eating enough red meat
being vegetarian
excessive blood loss from heavy periods, another hypothyroid symptom
donating blood too frequently (more than 3x/year) [22]
intestinal bleeding from something as simple as too much aspirin, or something as serious as colon cancer."
Gimel is the best I think to answer this.