Those are some good suggestions for dealing with allergy to dog.

Do make an appt with an allergist for skin testing for not only dog but for other things. Allergies can improve and worsen over time. All my life I have been severely allergic to cats but last year when I was skin tested again the doctor was stunned because I was hardly reacting to the cat and he gave me another shot of the control shot, histamine. Yay, I am getting better.

Since your symptoms have worsened since being with your dog it is possible that is the cause but immune systems do change so perhaps it is something else. Or the dog and something else.

Lots of options for asthma treatment available. I like albuterol nebulizers better than the rescue inhalers because it feels like the nebulizer gets deeper into my lungs.

Good luck.