Yes. The human body does kill its own cell sin the process of an allergic reaction. However, this process is part of the body's elaborate, complex, and well-coordinated immunological response to allergens. To keep things simple, the pain, rash, and swelling are the symptoms caused by the molecule known as histamine that is released by mast and immune cells. Histamine causes the cells of the blood vessels expand, which in turn causes the familiar symptoms. To do this process justice, I am going to include two free videos in the comments that goes into more detail about the immune response.