Son showing allergy signs to kitten?

We spent two hours at the shelter in a room full of cats. None of my children developed any allergy symptoms. On the way home, after we adopted the kitten of course, my son's eye turned red. They have been cuddling and hugging the kitten since we brought it home, and the kitten has just purred the whole time. My son's nose and face looks a little rashy, and it went away with benadryl. Any one know if he could adapt to the kitten over time? Am I putting his health in jeopardy by keeping the kitten? The kids are so attached already.