Brain fog and Iron Deficiency
Iron deficiency, even without anemia, can lead to many issues and symptoms in your body. Brain fog is just one of those.
It takes a while before iron deficiency manifests as anemia. Initially your regular iron stores including serum ferritin are utilized and then total iron of your body declines along with it.
Studies show that individuals who have normal hemoglobin may still be having very low total iron in their body and bone marrow.

Way forward? Get yourself tested for serum ferritin and at least total iron. If low, then consult your doctor for a supplement. It can either be oral or infusion, depending upon how much deficiency you have.
People have reported better concentration and no more brain fog after iron supplements. Also, your hair loss might be due to iron deficiency too and having iron supplements may reduce hair fall too.