I agree with DanceMom - a second set of eyes cannot hurt, especially when your child's treatment plan does not appear to be working. You don't have to switch to the second opinion doctor, or even follow their recommendations. It's just an opinion to see if there are other options.
We have done several second opinions over the years, and have even traveled to different states for them. It has been very worth it.
I would also say go with your gut. It sounds like you feel like something is not right with your girl (and given the severe anemia, I would agree).
Also, just wanted to add what we were told several years ago - iron injections are painful, that is why they use infusions more now, especially for kids. I just wanted to warn you, my daughter never had them so I can't say how painful. But our pediatrician told us they were painful and he was glad M would be having infusions.