Your low iron level probably means that you have anemia, or a drop in the red blood cell count. The red blood cells are important for carrying oxygen to all the cells in your body, including your heart. When your heart senses a drop in oxygen, it tends to beat faster and harder to help pump the blood to itself and to the other tissues in the body to keep the oxygen supply up. This may be the cause for your dizziness and sensation of the heart racing.
It is also possible that you are having a temporary abnormal heart rhythm known as an arrhythmia. Instead of the regular, steady heartbeat you should have, people with arrhythmia have an irregular heartbeat that can often be sensed as a racing heart, skipping beats, or pounding (palpitations) in the chest. Sometimes activity can bring on arrhythmias, but in some cases they also occur at rest as yours seem to do. During the time when the heartbeat is irregular, the heart may not pump enough blood to the brain and this can make you feel lightheaded.
It would be a good idea to have your blood count rechecked to see how severe your anemia is and also whether the iron is doing its job to correct your low iron level. Checking your electrolytes would also be a good idea since if they are out of balance this can cause an arrythmia.
An EKG test or perhaps a holter monitor (a heart monitor you weart at home for 24-48 hours to check for arrhythmia) would also be reasonable.
If you feel your symptoms are getting worse or you do faint, call your doctor right away.