Some patients have no pain during or after CoolSculpting, while others have some soreness and a few have great discomfort for a few days, and a very rare individual has extreme sensitivity that takes a couple of weeks or more to resolve.
The non-steroidal antiinflammatory agents including Naproxen, can help with this pain but can intensify the bruising that occurs. Furthermore, there can be medical risks with taking high doses of Naproxen, including the heart and kidneys, so check with your primary care doctor if you should or should not take the medicine, and at what dose. Also check wtih your Coolsculpting provider to ensure that it is oK.
The information provided in Dr. Shelton's answer is for educational purposes only and is not intended to constitute medical advice. The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs.
Web reference: http://www.thenyac.com/zeltiq/index.html