Your gum hurts because your upper wisdom teeth get into contact with the lower gums covering wisdom teeth which results in pain in gums, So the upper wisdom teeth is the culprit for the pain in gums...
So removing or incision of gums of lower part is a temporary relief... If u need permanent solution, then it is necessary to remove or extract upper wisdom tooth as in xray shown, you can see upper wisdom tooth is tilted and it is not in proper alignment so it hurts the lower part of gum....
Next Steps
Take secondary opinion and take your wise decision... thank you