Captom,
Good question, not durab. You are just planning ahead. When you have bad asthma like we do, it is natural to be worried about triggering attacks.
I've been to Yellowstone and the Tetons a bunch of times and never had any problems with the sulfur or other gases. Only a small portion of the parks attractions are actually around the springs and such. Lots of nature and natural wonders to see and explore. You know I have tons of environmentally triggered asthma problems too so I wouldn't steer you wrong. I think we went through some of our really bad times together.
The Tetons and Yellowstone are a great destination. Can I ask what state you live in? If you aren't used to it, it may take a bit of adjustment to the altitude. That may be something to talk to your Pulm. about. Some people have a bit more trouble with breathing at the higher altitudes, expecially when exerting themselves on walks and hikes. (By the way there are books with tons of short hikes all throughout the park. They will tell you the difficulty level and length of time for the hike so there is something for everyone. There is a great hike to some "Hidden Falls" at Jenny Lake.)
On the plus side, the humidity is fairly low and the spring and summer temperatures are pretty moderate. Very nice.
Have you decided on a time of year to go? Allergens could play a bit of a role too. If you haven't committed to a specific time, I'd recommend early spring when the pollens are still low. The weekend before memorial day when the parks open is cheaper and quieter. All the baby animals are out and about too. There is greenery in the lower altitudes and some snow up high. It's georgeous.
I agree with Titchou. If you are really concerned that you may flare while you are there it might be worth kicking up where you are on your asthma plan. For me, that would be increasing my Advair dosage in advance and filling my Prednisone prescription for a "just in case." I'd also use my Albuterol prior to any hiking.