What type of dog can I have that will not irritate my son’s eczema?

Dogs, and indeed any animals with furry or hairy coats (e.g. horses,
cats), shed their hair and skin into the environment. These small
particles are made up of proteins that are ‘foreign’ to humans. They
can irritate the skin without an allergic reaction taking place,
especially if the skin is already damaged with eczema. They may
also cause a genuine allergic response. Although breeds of dogs
with shorter coats may spread their proteins around the house in
lesser amounts, these will still be present in a significant quantity.
All dogs therefore have the potential to make eczema worse, so it
is probably best not to get a dog or other pet with a furry or hairy
coat.