Will swelling of the face and gums go way soon after root canal?

If Successful: If the root canal procedure has successfully removed the problem pulp tissue and sealed the tooth's canals, your body's immune system shoud be able to resolve the swelling. If the swelling doesn't resolve, antibiotics may be indicated or re-evaluation of the problem and/or treatment.

Generally, yes.: If all things go according to plan, pain and swelling generally start to subside immediately after a root canal procedure. However, the time involved varies from person to person and from tooth to tooth. Antibiotics and other medications can aid this process. Your dentist will determine if such medicines are necessary.