If the blood test shows that the iron levels are within range, even in the normal higher area.....Does that rule out anemia?

Anemia. While iron deficiency is a common cause of anemia esp in menstruating women, there are many causes of anemia with normal iron levels. Ie nutritional b vitamin defiency, bone marrow issues causing decreased production of red blood cells, hemolysis or increased breakdown of red blood cells, drugs etc. Your doctor should help sort things out for you.
Anemia. Anemia means the amount of red blood cells in your blood is low as manifested in low hemoglobin in your lab test. There are different kinds of anemia, and iron deficiency anemia is only one of them. So having high normal iron levels does not eliminate the possibility of you having anemia. You should discuss your concerns with your doctor.