My gums feel like they vibrating and its painful, could that be infected gums or the nervous system?

Vibrating gums: You may have a gum/bone infection, an abscessed tooth, a burn, an abrasion, or one of many other problems. To be diagnosed you have to be examined/possible imaging/possible lab tests. See your General Dentist or a gum/bone specialist, a Periodontist.

Gum problems: Start by seeing your regular dentist to determine cause and recommend treatment. We cannot diagnose problems over the internet sight unseen.