3 times a day does seem like a lot. Are you sure he doesn't have your lab work from another time. I personally refuse to take iron or prenatal with iron. It's a horribly constipation supplement. I do take in a lot of foods that are high in iron. (Greens, dried fruits that have a single seed, grapes, ect.)
I am 25 weeks and my doctor advice me to take 2x a day because when they check my lab test I need more iron.
My doc has me on it too since about 16w im taking 325 two times a day.