The recue dog may have had one of these problems which caused your reaction.
Dry skin can result in irritation and itchiness in the pet, which in turn causes even more dander to be spread around. Several common causes of dry skin in dogs, including poor nutrition, lack or improper balance of essential fatty acids in the dog's diet, overbathing the dog or using a wrong kind of shampoo (e.g. human shampoos or using a medicated shampoo too frequently), not brushing the dog frequently enough to release more oil to the coat, and several medical reasons (e.g. various forms of mange, hormonal disorders, fleabite allergies, chronic bacterial dermatitis).
In a rescue dog you don't always know the history of the animal.
I applaud you on rescuing dogs, what a noble thing to be involved in.