Can a person get asthma from environmental exposure?

Generally yes: One must have asthma or a tendency for asthma. Environmental allergies can trigger asthma , such as pollen, dust mites, and pet exposure. Non allergic triggers could be cold air, respiratory tract infections, air pollutants including cigarette smoke.

Can trigger: Certain elements in the environment can trigger an asthma exacerbation in someone who is predisposed or has asthma. But they do not "give" asthma to someone.