Hi E.,
Just like a lot of the other moms, my son also has allergies. He's had allergies since he was about 8 months old. You do need to get him seen as soon as possible. An accurate blood test that tests the antibodies as Melissa mentioned is best. Our allergist did it and it has shown that my son has allergies to egg whites, soy, wheat, oats, tomatoes, codfish, shrimp, peanuts (off the charts!), dust mites, cockaroaches, grasses, weeds, and more.
The hives could be something he's eating or wearing. You may have to change your detergent and put his clothes through the rinse cycle twice. He could also be allergic to his environment. Make sure his clothing is 100% cotton. Polyester, wool, nylon etc. could also make him break out in hives. Try to avoid giving him the common allergens with food like: milk, eggs, soy, peanuts...just to name a few. You can try to use oatmeal baths, but if he's allergic to it, it'll make the situation worse. I didn't know my son was allergic to oats until a 2nd blood test and I was always wondering why he would say it would hurt when he was in the oatmeal bath.
Hope you can find relief for your son soon!