How to make my gum swelling go away quickly?

Depends: Gum swelling must have an underlying cause to it. Looking for it and treating it will help resolve the swelling. If it's infection, an antibiotic may be needed. If it's associated with a procedure you may have had, you may need to call your dentist for advice. You can take an antiinflammatory medication, such as Ibuprofen or Naproxen (directions on the bottle) to begin with.

Go: You go see a Professional, a Dentist. With more than 10,000 hours of training and years of experience your dentist can determine the cause of the swelling (bacterial, virul, or fungal gum infection, abscessed teeth, neoplasm, allergic reaction, irritation from GERD, systemic disease, etc.). Once cause determined appropriate treatment can be applied.