When I was young, we LOVED our dog. When our dad showed signs of allergies, it turns out he was allergic. They put him on an inhaler. But, the problem is that if you suppress the allergy, it is still there, the body is UNHAPPY with the allergens. It ALWAYS continues to fester and develop into deeper health problems. Allergies are an AUTOIMMUNE response. If the allergen is left there, it develops into WORSE autoimmune problems, because the body is distressed and keeps fighting against these foreign attacking molecules. The body, over the years, always becomes sicker and more distressed.
This is the HONEST answer: you do not want the issues that come from worsening autoimmune response - it is the body in panic mode, and other sicknesses, diseases, and conditions always follow. Because it places such a HEAVY load of panic on the person's immune system. That is the HONEST answer. COVERING UP THE SYMPTOMS does not change anything.
DO NOT RISK A HUMAN BEING'S HEALTH FOR AN ANIMAL. Let's be honest. We have always LOVED, LOVED our dogs. I 100% understand. HOWEVER, let's keep things in an honest perspective: they are DOGS. The dogs LOVE us almost as if they were people, but they are not. They are not people: the honest truth is that they are Good Animals. But they are animals. If they threaten the long-term health of a human because of an allergy, don't risk your children's' health and life. The dog is a dog, it is an animal. A good animal, but still an animal. It can find another loving family where it can get used to and be perfectly happy. The honest truth is that you have to decide between an animal and the long term health of your child.
I am VERY experienced in this: allergens are something that ALWAYS, ALWAYS, ALWAYS without exception balloon and balloon. It is because an allergy is the body in distress. Do not cover it up with allergy medicines - they only mask the symptoms of what is STILL going on in the bloodstream and throughout the body. Long term use of pharmaceuticals also have an impact on the health of the brain.
NOTE: it might be an allergy to something weird that the dog was chewing on in the back yard. It might go away in a few days and never happen again. That would be possible, but unlikely. But if it doesn't go away and then never happen again, then it really truly is an allergy to dog saliva or dander.
The hard but honest truth is that you have to choose between the health of your child, and the inconvenience of your dog getting used to a different loving family. Always choose the health of the human. The dog will soon get used to another loving family. And you will prevent a lifetime of illnesses and worsening autoimmune and other health problems in your CHILD, the only thing that matters.