My hematologist specifically advised me not to take any iron supplements, this after I had transformed last year from ET to PV, tho I do take a multivitamin with iron with his knowledge and consent. I try to eat eggs in some form several times a week, as well.

I've asked for IV iron infusion after my anemia due to a massive bleeding and it worked amazingly, I've tried with nutrition supplements and diet but my stomach was too upset for it.
If you can choose ask for IV.