Low ferritin and low Vitamin D are extremely common with thyroid sufferers. You need to get both up to the higher end of your lab range.
Thyroid sufferers also can suffer gluten intolerance, with or without physical symptoms, and a lot have digestive disorders which lead to malabsorption of things like your iron and Vit d.
Vitamin D is important as it helps your adrenal function as well as uptake of T3. So all in all it's important for your thyroid help.
With thyroid conditions, not everybody suffers exact same symptoms, also most people will have other issues aside from their thyroid as it's kind of like a domino affect. Once one thing goes down it tends to take other things down with it. Putting it all back together is often like doing a jigsaw puzzle.
In my case i had very low vit D and ferritin,poor adrenal function producing too little cortisol, low digestive enzymes from my pancreas, poor phase 2 liver detox, excess estrogen and testosterone, low progesterone, fibroids due to excess estrogen, PMS, excessive fatigue, infertility, hair shedding and who knows what else at this point, but it's all part and parcel of the whole thyroid issue. I never feel cold, more warm than anything and i dont put on weight, but i'm hypo and have hashimoto's.
so make sure you keep and eagle eye on your ferritin, vitamin D and B12 too as your doctors likely wont give a toss and they are all important things in the whole process.
Hoping some of that helps and i'm sure you will find lots more informative information from the many posters on the board