You could get tested by an Allergist with what is called the skin prick test.
Or you can purchase blood work at a number of laboratories, online.
Some that come to mind:
http://www.lef.org/Vitamins-Supplements ... -Test.html
Also, in Terry Wahls' book Minding My Mitochondria, she says that she began a Paleo Diet, including Eggs, but never had blood work. I think she wavered a bit in her diet a year or so later, because she wasnt seeing any substantial results.
Then, she had bloodwork done and found to be allergic to Eggs, so she nixed them out of her diet. Its a fascinating book and her main argument is to do everything possible to cut down on unnecessary inflammation so that your brain's mitochondria can produce the maximum amount of ATP (energy) as possible.