What are the medical rules for asthma-type conditions and commercial airline pilots?

No, the rules are more lenient for commercial aviators. On a medical application you will have to disclose your medical history including any present medical conditions and whether you take a prescribed or unprescribed medication for them. You will also have to disclose any visits to see a doctor in the previous couple years as well as admissions to hospital, ever.

Since you have had problems with asthma in the past, the examining physician may have some questions and may be inclined to pay particular attention to your breathing. Many people, including myself, with a history of asthma at a young age eventually “grow out of it”. If there is any doubt, you may be required to take a treadmill test, a lung capacity test, or even be x-rayed for lung condition, but these would be unusual requirements.

Something which you would not know unless you’ve spent a fair amount of time in airplanes or very high in the mountains, is the effect of altitude on your condition, which could conceiveably be quite negative. The average airliner maintains a cabin altitude of between 5,000 and 10,000 feet, so if you have been an occasional airline passenger with no negative reaction, then you’re probably OK.

However, I suggest that you consider consulting an aviation physician prior to applying for an airman medical certificate. While there you might inquire as to whether being tested in a hyperbaric chamber (where they reduce the air pressure to simulate high altitudes) might be warranted. It would be a shame if you spent a lot of money on flight training to find out that you could not pass the medical requirements or had an unforseen problem with high altitudes.