There is no such thing as a "blood allergy." It's possible you're asking about an allergic reaction that involves symptoms like a rash or hives, which can be caused by a variety of things, such as certain medications, foods, or insect stings. These symptoms are not directly related to the blood itself but rather to the body's immune response to a specific allergen.
If you're experiencing allergic symptoms, it's important to consult a doctor to determine the cause and receive appropriate treatment.