As you suspected, you should definitely get in to see your dentist to have this checked out.
The most common cause of gum swelling is something called gingivitis. Gingivitis is inflammation of the gum lining at the base of the teeth. The most common cause of gingivitis is collection of bacteria and food debris between the gum and the teeth. Mild cases of gingivitis will respond to increased dental hygiene (regularly, daily brushing and flossing) to remove the debris. More severe cases may require a deeper dental cleaning
, which can be performed in your dentist's office.
The reason to get this checked out soon is that severe gingivitis, if left unchecked, can lead to severe damage to the teeth as the gum line erodes away from the inflammation. Also, severe gingivitis can be a source of infection, whereby the bacteria in the gums get into the bloodstream and infect other organs in the body.
If you are not very good at keeping up with brushing and flossing, you should start to do that right away. Your dentist will them be able to determine if this is indeed gingivitis and, if so, what other steps need to be taken to clear it up.