Can an infection in the mouth possibly from a cavity make the neck swollen?

Mouth infection: Yes, the infection can cause the lymph gland in your neck tonswell.

Neck swelling: You can definitely see neck swelling from a dental infection. These infections can be particularly nasty, so i would suggest seeing your doctor immediately. Feel better.

Yes: Dental infections can cause both swollen lymph glands or even infections in the soft tissues of the neck.

Time to go to Doc!: Absolutely! untreated dental infections spread to the mouth & facial soft tissues as well as bones. Sometimes infection spreads through 'potential spaces' in the muscle/soft tissues to the neck, the tissue space around the vital blood vessels in the neck & from here to the brain or lungs. Can be a slow growing bug but sometimes are aggressive life threatining (actinomycosis vs. Lemmiers disease).