I'm sorry if this sounds harsh, but I honestly think there is nothing that you can do if you and your son are allergic. I consider yorkies to be more allergy friendly vs hypoallergenic. I'm allergic to anything fluffy and cute, but it seems I'm less sensitive to my yorkie. I'm still allergic, but since it's just me, it's something I can live with since he brings me so much joy in return.
I really hope it's just the shampoo. A shampoo that the groomed used made me itchy, and another I tried made me break out I hives. I'm very sensitive, but somehow, Kaji and I make it work.
I hope I works out for you too.