cool sculpting can burn the skin theoretically as super cold can burn skin similar to heat - however, if done properly, the risk should be very rare- I have never seen one personally- I would follow up with your provider to see if it is a burn - this should not affect the fat freezing
You should not get any type of burn from coolsculpting. Redness of the skin is typical following the procedure. The machines themselves have a built-in safety mechanism to turn off if there is any type of exposure of the skin to the cooling itself.