There are some allergist that don't use the needle/prick provocative testing. They use a lucite bar that you hold and the machine notes whether you have a electronic change/allergy...
I wouldn't go to just any allergist though, but that's me. I also wouldn't put up with congestion. Been there, done that...ended up with nasal polyps that had to be surgically removed.
Yes, washing walls, floors, drapes etc helps too.
(When I was little everything was plasticized...but back then they didn't know I am allergic to petroleum based products (plastics.) But the smell of new plastic can get to you too...
Get rid of clutter and dust catchers. Keep table tops ..dressers etc clear. Wipe things down with damp cloths to keep from flying the dust and dander around.
Just don't let the dog sleep in the bed with you... and if you can, don't let it sleep in the room with you or be in your bedroom. I think that will help immensely.
"Get rid of the dog." Sigh imagine!