Is it safe to use nebulizer for baby cough ? Anybody use then baby get asthma ?

Yes nebulizer is safe. In fact it should help to stop your baby from developing asthma rather than the other way round. Usually nebulizer is not prescribed to baby as the first round of defense though unless baby has loud heaving sound or difficulty breathing. If you let baby's cough go on for too long and too much phlegm she may develop bronchitis which will make them more prone to asthma later on. If your PD recommends the use of nebulizer I think he has reason to do so and it is safe