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It is certainly true that the low haemoglobin can cause these symptoms, because the red blood cells carry oxygen throughout the body, including the brain, and when there is insufficient oxygen, then every organ in the body may not work properly.
There are many possible causes of a low haemoglobin or anaemia. It is true that one of the most common causes of anaemia in young adult women is iron deficiency from blood loss during periods. However, you are correct that if you are not having periods since the haemoglobin was 12.8 in Dec 2014, it cannot be blamed on the periods.
It is possible that it could still be iron deficiency related to other sites of blood loss, which if not readily apparent, is usually in the gut such as from ulcers, vascular abnormalities, inflammatory bowel disease, or growths. There are other nutrient deficiencies that can cause anaemia, such as vitamin B12 or folic acid deficiency. It is also possible to get anaemia because of increased breakdown of red blood cells, such as from haemolysis.
The cause of the anaemia cannot be identified from the haemoglobin level alone. There are many other tests that would need to be done to determine the cause of the anaemia. Your doctor should have already started performing additional testing once it was learned that the haemoglobin was 7.5.
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Rechecking the haemoglobin in 4 weeks is to see whether it is getting better or worse, but the additional testing that would identify the cause can be done at any time.
The first steps in the evaluation for the cause may have been ordered on the blood that was already in the lab. The red blood cell indices would be part of the blood count. They also can do an analysis of a peripheral smear. They can measure reticulocytres, which are young red blood cells, to see if the bone marrow is responding to the low haemoglobin. Further evaluation would be guided by these findings, and may include an iron profile, vitamin B12 and folic acid levels.
It is good that you are eating a healthy diet. However, a healthy diet is not sufficient to prevent every nutrient deficiency. Iron deficiency primarily occurs because of blood loss. Iron intake in the diet only becomes an issue if there is blood loss. It is virtually impossible to become iron deficient solely by eating too little iron. A person would develop far more significant deficiencies in other nutrients before they would become iron deficient from a poor diet. In addition, people develop vitamin B12 deficiency because of a defect in absorption of the vitamin. So, eating a healthy diet will not alter whether the gut will absorb the vitamin.
The anaemia would not be an absorption problem if the vitamin B12 and folic acid levels are normal. In the same way that iron deficiency does not occur solely from a poor diet, iron deficiency also does not occur from poor absorption.
If you were placed on iron supplements, that would suggest that the evaluation showed iron deficiency. If there is documented iron deficiency and you have not have periods since the normal haemoglobin in Dec 2014, then there should be consideration of an evaluation for a site of blood loss, which usually would involve an upper and lower endoscopy of the GI tract.
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