H pylori/low ferritin level.

Hello Doctor, My serum ferritin level is 4 ng/mL, and I have been experiencing significant hair fall. I am also currently undergoing treatment for H. pylori infection. My doctor in Bangalore mentioned that my iron stores are severely depleted and recommended an IV iron infusion (Ferric Carboxymaltose 500 mg). However, I recently consulted a doctor in Coimbatore who mentioned that a ferritin level of 4 is normal and that my hair fall could be due to other reasons. He suggested taking oral iron supplements instead. I would like to know whether a ferritin level as low as 4 can be effectively corrected with oral iron supplements, especially while undergoing treatment for H. pylori, or whether an IV iron infusion would be more appropriate. Could H. pylori infection also affect iron absorption and the effectiveness of oral iron supplements?