What are the types of allergic reactions? do they always result in hives?

No: There are many types of allergy and not all result in hives. The more talked-about type involves IgE-antibody and these reactions commonly involve hives (but be careful, hives do not equal allergy). IgE is a form of "memory" for the immune system. Another form is T-cell (a white blood cell) that is involved in "delayed" allergy (eg poison ivy, some sulfa reactions) usually with diffuse rash...