Gas pain should have nothing to do with Coolsculpting. Delayed onset of pain from Coolsculpting usually occurs within the first week or two. You usually feel this in the skin tissue. If you are feeling gas pain there is something else happening and you may want to consult your doctor.
It would not be a side effect to have gas pain after coolsculpting, especially one month later. I suggest you consult with a GI doctor to determine the cause of your gas to help best treat you.