Hey there! I hope you're fine, and made it through the night ok.
I am a person that is allergic to dogs, including my hypoallergenic yorkie. Somehow, we manage to coexist just fine. First thing I would do in your shoes is bathe the puppy. Normally I don't recommend this, but since it's a new puppy, and maybe your reaction is to her shampoo, bathe her/him in your shampoo. Wash everyhing the puppy has touched as well. After that, select a shampoo very carefully, as it will be your life saver. I really like yorkie splash and shine, I have had 0 reactions to that, or for a quick fix, Nootie is also a good shampoo and it can be found at Petco.
Nootie is my go to shampoo when I run out of splash and shine, as slash and shine can only be ordered online. (so far)
I understand the heavy chest feeling as I use to get them all the time. I started bathing my boy twice a week, and it's made all the difference. His coat and skin have not suffered any ill effects, and we can stay a happy family.
Good luck!