Hello Doctor, My 12 Month Daughter Has Mild Coughing With

Hello doctor, my 12 month daughter has mild coughing with phalgum and vomiting as she eat/drink anything ,since 4 months. now docter has given budcort and asthalin inhaler with spacer 4 times a day, montina-L half tab at night. also had tried different antibiotics and neublisers previously. is it safe? is it asthama? forever? how long to continue inhaler is not habit forming and safe.