Is it possible for a 10 month old baby to have asthma? symptoms?

Yes. Some risk : factors in full-term babies are bronchiolitis in infancy, family history of asthma & allergies, early introduction of allergenic foods, sometimes from repeated exposure through breast milk, & environmental smoke. Asthma is characterized by recurrent wheezing caused by bronchial spasm in response to viral upper respiratory infections, allergens &/or irritants that responds to bronchodilators.

Maybe: Not everything that causes wheezing in infants is true asthma. Many will wheeze with a lower respiratory virus infection in infancy, like RSV & these kids can have recurrent wheezing for up to a year & with URI's. By age 5, 3/4 have quit & never wheeze again. A strong family history of asthma & wheezing in the absence of a chest infection will often be the earliest sign of true lifelong asthma