Susan,
i too have asthma and needed to get a 'hypoallergenic' dog breed. The ones I know of for sure are poodles, maltese, sh*tzu, bichon frise, poodle crosses (ie shipooh, maltipooh, cockapooh), and chinese cresteds. I would recommend allowing your son to hold/pet any dog before bringing it home. The only allergic reactions I have to my chinese crested is when I clean his ears or eyes without washing my hands immediately afterwards. Hope this helps!
Jody