I have a terrible time with iron supplements and was told to quit taking them. My friend with many years as a medical professional, told me to start on folic acid tabs asap last summer when I was so anemic. She told me it would bring up my hemoglobin lots faster and safer than iron. It did. You might want to ask your docs about it. It is an over-the-counter vitamin supplement and in my experience, did a much, much better job than iron tabs and I was to the point where they were threatening me with a transfusion.

Also, have they checked your pulse oxygen? That's the little thing they put on the end of your finger with a digital gauge which will tell them how much oxygen you have in your blood. From what I remember, there is something about low blood oxygen and red blood cells which may contribute to breathless feelings. It's something easy to check and treatable.