Swollen gums can be serious. If you have an absessed tooth, the infection from it goes directly to your heart.
I have a heart condition known as mitral valve prolapse, and I have to take medication before I even get my teeth cleaned because the bacteria goes directly to my heart. Take the suggestion to go to a dentist and have them take a look at your mouth.
If you've had flu or some illness that's causing you to vomit, it could be a reaction to the stomach acid reaching your gums, and it can cause all kinds of problems. See a professional, and gargle with salt water (don't swallow it).