When I take oral antihistamines I get hives over my entire body. Is it possible to be allergic to antihistamines? What can be taken instead?

Unlikely. Each antihistamine is unique, so it is unlikely that you would be allergic to multiple antihistamines. I had one patient who had hives to an antihistamine, and it turned out to be an allergy to a dye. You should consult with someone familiar with these medications and medication reactions in general, such as an allergist.