I have low hemoglobin/hematocrit but my iron levels are that of a healthy person; a liver problem?

Unlikely liver... There are many causes. Anemia (low hemoglobin) is caused by the body losing blood (heavy periods, blood in stool, red blood cell instability [hemoglobinopathies] or destruction [hemolysis]), the bodies inability to produce new red blood cells (for example iron deficiency), or a combination of these. Many causes of anemia are treatable, and some are inherited (sickle cell).
Anemia. The list of things that can cause anemia is too long to list here, but it includes many other things besides iron deficiency. It is important that you undergo evaluation by a hematologist in order to receive the correct diagnosis and determine the appropriate therapy.