Hi mcdc,
Welcome to the Asthma Club!
Sorry to know that this has occurred for you.
Since I am not in the US, I will not comment on the meds and your costs, but I can give you my life experience.
I understand from my many doctors over my 72 years, that allergies can disappear and re-appear at will !! They also can become much worse. There is no way to know the whys and whens of it all. We just deal with the present.... that keeps us busy enough.
It is very helpful that you can trace your increase in symptoms to getting your new dog. From your history it would seem apparent that your new bundle of joy is the culprit for your declining health. This brings the sobering thought of what actions you may need to take to help your own health.
This gave me tears as I re-called my loss of my beloved dog, after a life-threatening asthma attack. It was a great trauma to my 13 year old self.... but I lived to tell the tale!
But, before you do anything that drastic, I would suggest you visit your doctor again and ask about allergies to animals. Possibly, your asthma is due to something else.
Hopefully and just maybe, you will be able to mitigate the impact of the dander with allergy shots or routines of dog baths, washing his bedding, etc. Although, I would think, your allergist will be very concerned if you choose to keep your dog.
I send you all the best for the discussions that will follow with your doctors.
There is a phrase often repeated about asthma... "When you can't breathe, nothing else matters" How true.