Yes the snubber will help!

also
  • Make sure you have connected both PIC VSS pins.
  • Make sure you have disable the LVP mode
  • Set all unused i/o to input and connect ALL of them to GND
  • i would add a 47-220 uF on the PIC VDD line as well (close to the PIC)
  • Place your PIC away of your relay to see what's happen.

How much current do you drive on the AC side?