Not exactly. She lost her organs from her stomach down (about), but the other organs have been working to keep her alive. When she exerts herself, it stresses the organs and she bleeds internally.
O.o Ummm well it's because she used alchemy to try to bring her baby back to life. She ended up losing some organs, so she coughs up blood every now and then. They explain that in the anime ~_~;
Izumi lost her reproductive organs, remember in the manga when ed asked why she didnt have any children? She lost her organs tring to bring her dead baby back by using human transmutation.