Sudden sharp-shooting pain at the gums around my wisdom tooth especially the back part. not sensitive to touch and temperature. ?

See a dentist: See a dentist to evaluate not only the wisdom tooth but the adjacent teeth and surrounding gums. We can't diagnose or treat you over the internet. This requires a one on one clinical exam and x-rays by a local dentist.

Gum infected?: Could be pericoronitis, an infection/inflammation of the tissue surrounding the wisdom tooth. Food may have been trapped there, broke down and an infection has occurred. Hard to say, though. I would get to a dentist/oral surgeon asap before it flares up.