Can a blood transfusion give you new allergies?

Very Unlikely, but..: ...Not impossible. First, there is the possibility of a reaction to the transfused blood itself, in spite of type and crossmatch; second, a very small amount of serum remains with packed red cells (the most usually transfused part of blood) and it contains the donor's ige, the allergic immunoglobulin, which may contribute to a mild, temporary, and very rare new allergy.

No : A simple blood transfusion should not lead to new allergies. Interestingly, it is possible for those who undergo a bone marrow transplant to develop new allergies.