Tonsillitis is bacteria infection of the tonsils. It is caused by bacteria usually present in the mouth or from the nostrils and airway.
Prevention is same as prevention of bacteria infections... Good personal hygiene, adequate nutrition and immunization against the bacteria where feasible... HIB AND PCV13 vaccines for examples.
Treatment of upper respiratory tract infections promptly can also prevent spread. Children with enlarged tonsils are prone to Tonsillitis especially the recurrent Tonsillitis and may require tonsillectomy as permanent solution

Tonsillitis on its own does not affect breathing. I guess your baby may have additional issues for example adenoids enlargement

Tonsilitis is an infection of the tonsil. it could be from infection of the mouth or the nose. If your child has tonsillitis he or she needs to be examined by a pediatrician.