I've had asthma like you but I've never been told that anything to do with my nails was directly linked to my lungs. However, my mother was recently diagnosed with asthma as well and her nails do the same thing your's are doing. I have vertical ridges on my nails and they do wave but they don't curve under. Most commonly the doctors have told me its a vitamin or mineral deficiency. I've tried multi-vitamins, cutting caffeine from my diet, and improving what I eat on the whole. Nothing has really made all that much of a change in their condition. Good luck. If you find anything out let me know.