Low ferritin can interfere with the thyroid's 'job'. TSH goes up and down as many as three whole points in any given day in any given human, it is NOT a test for thyroid.
Ft4 is generally acceptable when medicated to midway of it's range (about in the middle, mine is slightly lower but I feel well), Ft3 is generally acceptable when about 2/3 or higher, depending on the person, their hormone status (are you 30, are you 65??? Perimeno, meno...???) and I like MINE at around 3/4 of the range or higher.
If your lipids were high, sometimes that can be a 'marker' for having thyroid disease. I do NOT see the test for the most common type of hypothyroidism (TPO AB) so you'd want that...ferrtin in that range...you'd want to see it higher than that...my labs' range is 10-210 and my doctor wants it at 70 at LEAST but not higher than around 150...but that's MY thyroid doctor.
I have seen patients with TSH's of over 160, and they felt great, and were athletic, and I've seen (and been) patients with a TSH of .22 and they could barely drag themselves in the door for testing. So, TSH is NOT a reliable test for hypothyroidism.
You need a Thyroid Peroxidase Antibodies (TPO AB) to test for autoimmune Hashimoto's. Most of us (I've been a thyroid patient advocate for 22 years, but recently retired as I am facing some disabilities of my own) see FIVE doctors before we find ONE who will treat with both T4 and T3. There are lists of doctors on the net (google: top thyroid doctors) and just screen carefully the patient recommendations...look for 'The doctor tested everything and KNEW to give Armour Thyroid, OR T4 and Cytomel'...not rec. that say 'OOOH, AHHH, he was CUTE and listened!!!' (and then did nothing)
Best of luck to you!