I have an allergy to cat hair and dander, and we succesfully kept two cats inside for many years. It all depends on the severity of the allergy, and allergies can wax and wane over the years depending on the degree of exposure to the allergen.

You may be able to look at a densisitisation program, where they use small doses of the allergen over time to slowly reduce the severity of an allergic reaction. But your DS would probably have to be older. Another option for him when he is an adult may be a long-term steroid to manage allergy symptoms; I have been on Nasonex on and off for probably 10 years now to help treat seasonal allergic rhinitis that used to be so bad I would have a runny nose and itchy eyes for weeks at a time.