Can heavy periods lead to decreased hemoglobin and anemia?

Ive been suffering from some pretty heavy periods since I started at age 11. 4 wks after I had my daughter via c-section I experienced 2 gruesome periods 2 weeks apart..at that time I saw my OB and she said that period blood loss usually does not cause anemia. Everytime I go for a check up and get blood work done at my GP I am always anemic..I try very hard to stick to a multi-vitamin/iron supplement but it seems they both irritate my stomach..Any advice ladies? I know birth control is an option to decrease heavy periods, but I would prefer to stay off them.