Yes you can be allergic to your own sweat and break out in hives.
Some people who are allergic to their sweat will break out in hives and may have other rashes and itchy skin due to the sweat.
Nerve fibers in your sweat glands can cause an allergic reaction to your sweat so if you're sweating and are getting itchy or rashes you should make sure to clean the sweat off your body as often as you can.
Even using a wet washcloth to clean the sweat off you often is a good idea.
There's not too much else you can do if you are allergic to your own sweat.
But it's rare that a person is allergic to their own sweat but some people are.