Anemic with Super Light Periods - Find a cause?

So when I was diagnosed with anemia about half a year ago, all I was told was take some iron pills. I was also told I should only take every other day. I think everything was pretty low, low hemoglobin, iron saturation, and ferritin of 10.

What's been bothering me is, I know that they just assume because I'm a woman it's heavy periods (and I know it often is). But I have extremely light 1-2 day max periods that happen less than once a month.

I'm thinking of going back to the doctor (we never planned any follow up) and pushing a little on investigating the cause since my periods barely exist. I'm also still experiencing a lot of the same symptoms still. However, I already get the feeling this doctor just thinks I'm anxious and crazy, and I don't want to be pushy if this is normal and I'm overreacting.

Thoughts? Also should I really only be taking iron every other day?