i'm allergic to dogs but we had a Toy Poodle growing up and I did not react to her. We also had a cockapoo and I did not react to him.
Most doctors will tell you no because they don't want it on their heads if your son has some type of big reaction. If you choose to get a dog and and he has a reaction, the doctor will say "well, I advised against it." It's just a way of him covering his tail because people are so sue-happy nowadays.
If you do choose to get a dog, be sure to discuss ahead of time with your son that the dog may not be able to stay and give it a trial period.
Do not let the dog in your son's room. He should sleep away from the dog at night. Invest in an air cleaner in his room. Keep the dog clean, you will probably have to bathe it. You can bathe it in shampoo that will help keep the allergens down.
it's not true that being around an allergen will always make you more allergic. I grew up severely allergic to cats. All I had to do was walk into someone's house that had a cat and my eyes would water and my throat would close.
Then my boyfriend had a low-dander cat. For some reason I was not very allergic to her. Ever since then I've not been allergic to cats and we have two. Allergy treatment often entails exposing a person to small amounts of the allergen so you can build up immunity. I think the low-dander cat did that for me.
I will say that I am more allergic to dogs now that we don't have one. When we had a dog my allergy was slight. Now it's as bad as my cat allergy was--and my cat allergy shows up on allergy tests but I'm not allergic to MY cats.
You don't know what will happen with each individual person. Your son could become worse. It's all in what you're willing to risk---and how much responsibility you're willing to put into keeping the dog. My husband is allergic to my cats so I put in A LOT of work so I can keep them. Be prepared to do the same.