I have effort-induced asthma and it has never made me feel sick to my stomach, even when I cough a lot. Pain in the lungs and bronchi, yes. Wheezing, yes. But never any nausea. Could be it's just anxiety because of the asthma that is making you feel ill. I do agree about seeing a doctor, but I don't think you will v* from this if you try to relax and take something for your cough, like warm water with honey and lemon. That will soothe you a bit.