Is it possible for my 4 year old son to be allergic to our new puppy even though we've had a dog for 2 years?

We've had a golden retriever for 2 years. Last week, we adopted an Australian Shephard mix. My son broke out in awful welts all over his body 5 days later. The doctor says it's definitely an allergic reaction. I can not think of any new products, foods, or substances ingested or consumed during that week. Is it possible for him to be allergic to the new puppy and not our old dog?