Iron//nutrient deficiencies are common in hypothyroidism due to gut malabsorption issues (hypochlorhydria).
Both T4 & FT3 just over halfway through range. Most medicating Levothroxine function better with hormones in upper third of range. This doesn't always mean you are under medicated but that maybe the meds are working properly.
Your Vit B12 result is only shown as "normal". A doctors "normal" may not be the same level as that which members have found to be most beneficial for good thyroid function. Your Vit B12 result should read at least 500 but nearer to a 1000 is preferable.
Your Ferritin is not " normal" but deficient as results are under range ! ! . The body needs iron for carrying oxygen throughout the body and to assist in digestion (enzymes), but more importantly when levels are low it slows down the conversion of T4 to T3 (deiodinase activity) as requires iron containing enzyme Thyroid Peroxidase to produce the thyroid hormones ...... ... .so impairs good thyroid hormone synthesis.
Optimal ferritin levels are usually about 70 -90 so you will need to supplement. Members supplement Ferrous Fumarate, taking each iron tablet with 500mg-1,000mg vitamin C to aid absorption and minimise constipation. I don't supplement iron so repost a question re dosing.
Consuming dairy products, coffee, tea, chocolate and eggs with iron can interfere with the absorption. Medicating antacids, proton pump inhibitors (to treat acid reflux) or calcium supplements with iron can inhibit absorption.
Ask your GP to retest after 6 months and take the tablet four hours away from Levothyroxine to prevent it from binding and reducing thyroid hormone availability..
..[... painful legs and muscles, sometimes shortness of breath, dry skin in hands, legs and mouth, dizziness and low heart rate ..]... can be symptoms of low thyroid hormone but also nutrient//iron deficiencies. Post your Vit B12 result. Have you had Vit D & folate tested ? .
Iron & Thyroid connection
Thyroid & Important Nutrients