Hi dip1973 and welcome,
The bilirubin level rises as red blood cells are filtered out and destroyed by the spleen. As you have seen, this process accelerates when the child is ill and the Hb drops. The bilirubin is a by product of the break down of the red blood cells and is not much of a concern. I would advise to try the hydroxyurea and folate program, as this can raise the hemoglobin level and may also help slow the breakdown of the red cells. It does require some patience, as the effects of hydroxyurea can take two years or more before the full effect is seen. This program is a good alternative to transfusion, and since the Hb level has dropped as low as 6.5, some action is required. I will also mention that hydroxyurea has a stronger effect when magnesium and L-carntine are also added as supplements. Our moderator, Manal has a son on hydroxyurea and may have some advice on the dosing.
How old is your son?