Save your voice while being sick but it gets blurry with allergies and asthma. I can hear an allergic reaction from my voice before I can feel anything, like playing Singstar and a pet visiting. The volume of lungs can greatly vary during allergic season from more normal. So how should you train singing with allergies and asthma?
I believe practicing or singing during an allergy or any infection is very dangerous as it gives a lot of strain to the already strained muscles of the throat. A proper medication is really required to recover. Yoga, meditation and breathing exercises really help for singing. Either ways, a good exercise and a good balanced diet is required to maintain a good voice and good health. A humidifier is required since it helps keeping the air moist. You'll definitely bounce back once you regularly practice after the recovery of asthma or allergy.
Happy Singing :)