This is an excellent observation on your part. While iron is an important part of treatment in patients with anemia, there is such a thing as too much iron. I do not routinely recommend multivitamins in young people unless their diet is lacking in certain areas. In your case, I think that it would be best for you to search out a multivitamin which comes without iron, just to be safe. This way you don't have to worry about overloading yourself.
Keep in mind that you will still need to have your iron levels checked periodically when you are on iron supplementation. It would be a good idea to have this done a few months after starting iron to make sure that you are getting enough and not getting too much. Iron pills can make you constipated and you don't want to take too many if you don't need to.
Before starting any new vitamin, mineral, or new over the counter medication, be sure to ask your doctor if it is safe. The best doctor for you to bring this up with is your primary care physician
or internal medicine doctor
). He or she will know your past and current medical conditions the best and will be able to make a decision that is in your best interest. Good luck.