You certainly shouldn't be eating any more chicken; your body is trying to tell you something when it reacts so strongly. Allergies can occur at any time for no apparent reason. I've just found that I'm now having allergic reactions to fresh cherries; go figure. Have you had the same type of reations to other foods that contain chicken such as hot dogs, soups, or sauces made from chicken stock?
In any case you should follow your doctor's advice. He should be made aware of the full extent of the allergic reactions including as acurate a time line of events as you can recall.