If you are required to daily medicate to control, here that is not mild asthma, just well controlled asthma if you havent had an attack for a long time. Any mild attacks requiring use of medication of late?
Have you seen an asthma specialist lately. Might be worth paying a visit to see how well your body is coping. As for dust... there is usually lots on the flight deck! Not being discouraging, but one would hope that the doctor you saw doesn't make a habit of ticking medicals okay, when there is something amis, albiet slight...
Its not my place to question the Drs thought processes as I dont know him or your history. But Ive seen a slight heart murmur walk out, mis-diagnosed as "just getting on a bit", and have a fatal infarct getting out of the cockpit 3 hours later (no stress VFR non CTA flight). The passengers tried to revive him. Drastic story I know, and rare, but the Dr thought he would sign him out anyway, without doing the ECG even though it was required as the irregular pulse it would have shown may raise some eyebrows back in CASA medical office. That Dr has since retired.
Its not the diagnosis in this case that is at fault, but the lies will bite! In my humble opinion you were sufficiently worried to ask on this forum for advice, so recommend the following - talk to the asthma specialist and another aviation Dr, take your report from him back to the CAA and get it sorted..... you dont want to loose a perfectly good job over a little lie!