I asked the same question when I began my Thyroid journey.
The answers I received all said that hypothyroidism is likely causing absorbption issues resulting in the low Vitamin and Mineral blood results. These deficencies are very common in thyroid disease and they should improve once adequate thyroid hormone level are reached.
(Because the thyroid regulates the metabolism in virtually every cell in the body). .
On the flip side, low ferritin (anemia) and being low in the B vitamins can give you symptoms very similar to hypoT.
My ferritin level was around 10 at the time (should be at least 50). I also had really low Vitamin D (22) and B12 (323)
I began supplementing my iron (taken with vitamin C for best absorbtion), vitamin D-3, B Complex 50 and sub-lingual B12. B's were easy to get optimal, but I still struggle with the ferritin and vit. D. But I'm no where close to being optimized in Thyroid levels yet either.
Since you have labs stating you are low, I would start supplementing your iron now. Being anemic can cause you to feel quite tired, short of breath, weak muscles etc.
Hope this helped answer your question.
Edit: Please know you need to take any iron supplements a minimum of 4 hours after taking thyroid hormone.