This word works two ways. As an adjective it means “to do with asthma” or “having asthma”: an asthmatic child, an asthmatic cough. That use is still normal in medical English and in everyday speech. As a noun, an asthmatic is a person who has asthma. You will meet the noun in older writing and in some medical notes, but many people now prefer “a person with asthma” or “someone who has asthma,” because the noun can sound as if the illness is the whole person. You should recognise it; you do not have to use it about someone. There is also a loose, slightly unkind use: calling a sound asthmatic when an old engine wheezes. That is picture-language, not a doctor’s word.