When you have inflamed gums it means that you likely have a tooth or gum infection that should be looked at by a dentist.
If you want to just wait then the inflamed or swollen gums should go away after a week or two but if not I would see a dentist about it.
The Listerine can help keep your mouth clean of bacteria and prevent further tooth infections but it won't help get rid of inflamed gums.
Dentist treatment can get rid of the tooth infection or gum infection get rid of the inflammation of your gums though.