The symptoms of a wool allergy are usually skin irritation such as an
itchy rash. These symptoms could also be caused by laundry detergents or
I react to these common chemicals but have no problem with wool.
Some people are actually allergic to the animal proteins or the oils from its skin. Just like people can be allergic to cats or horses, people can actually be allergic to sheep or their lanolin.
The answer? Give some other animal species a try! Just because you're allergic to sheep doesn't mean you're allergic to buffalo.
The book No Sheep for You by Amy R. Singer has some great patterns using other fibers.
Sometimes it is also a matter of how course the wool is. If your skin is sensitive to course and stiff fibers, it will become irritated with an itchy sensation. In this case, try using a finer wool breed like Merino.
Sometimes the reaction is actually to the harsh chemicals sometimes used to remove lanolin and add dye. The allergic reaction could also be caused by a chemical used on the sheep such as an insecticide.
If you react to wool, I suggest you try exposing yourself to organic wool yarn or organic unprocessed wool fiber. Obviously, you shouldn't try it if your reaction is severe and could cause anaphylactic shock, but running some little exposure tests is exactly what an allergist doctor would do.
If you still react, avoid wool yarn and use alternative fibers for crafts. There is an alternative available for every property of wool except felting, but that can be achieved with some other animal fibers such as angora.