Hi Rozitka and welcome to the group,
The word your doctor used is hemolysis, which is the break down of red blood cells. This happens after transfusions as the body begins to break down the freshly transfused red cells. If your spleen is enlarged, it is a sign that your spleen is overactive and breaking the red cells down even faster. If your spleen is not severely enlarged, there is no reason to remove it. If it is quite large, then there is a risk of the spleen rupturing, which is very dangerous. The size of your spleen is easily measured by a physical examination by your doctor. Has your doctor told you your spleen is enlarged and if so, how big is it? If your spleen was causing a serious problem, I don't think your blood would last three weeks between transfusions. The yellow in the eyes is bilirubin, which is the product of hemolysis. Using only packed red cells can limit this reaction. Proper matching of the blood antibodies can also reduce this. The use of a cortisone drug, such as prednisone can also reduce this reaction. Since your blood is lasting three weeks, I do not think the problem is severe.
Removal of the spleen is often a standard practice with thalassemia, but the results have not been consistent. It does help reduce transfusion frequency for some patients, but not all, and in some where it does, the frequency eventually becomes the same again, and the result is that removal of the spleen gave no long term help. I do feel that the spleen should not be removed unless it is seriously enlarged and presents a danger.