Should I be worried about getting too much Iron?

I am pregnant and have mild Anemia (my hemoglobin is 8. 25). I went to see a hematologist to correct the problem. I was trying to treat the problem naturally but my iron levels didn’t increase at all. I started to take some iron tablets since the natural things weren’t working and my hemoglobin went from 8.25 to 9. something in 2 weeks. The hematologist has recommended an intravenous Iron treatment to get my levels up to where they need to be for delivery. I would be placed on an iron drip for ½ hour 3 times a week then my iron would be checked. I’m just worried that i would get too much iron. I read some where that too much iron can damage your organs. I am due in Sept 23 and need to get my iron levels up quick! Do you have any recommendations or any experience taking intravenous iron treatment?