Coolsculpting is an absolutely safe treatment, acting exclusively on local fat, without affecting the surrounding tissues (skin, vessels, etc.). Coolsculpting, as all medical treatments, may have side effects on certain people. Numbness of the area is one of them. Often a tingling sensation is evident at the area after treatment. In addition, you may notice redness in the area or, more rarely, bruising.
All these reactions are absolutely normal and safe, and they resolve really quickly.