I swallow a piece of gum (on accident) and it feels like its still there how can I make it go away?

See a GI. Gum usually doesnt stick in the throat unless you have an obstruction. If you can eat other food there is nothing to worry about. If you can't swollow solids and or liquids go to a gastroenterologist. You may nned an endoscopy if it persists.
Try some water. It may still be stuck either in the back of your throat or esophagus. Try some water which will help to wash it down.