Thank you for your question. The best way to maximize the benefits of CoolSculpting is to maintain a healthy diet and exercise regimen. There is evidence that any of the other methods you have mentions would help remove any extra fat. Please talk to your treating physician before taking any...
You need to be seen to determine which procedure is best for you. There have been great results with CoolSculpting around the armpit if your skin has good elasticity. Good luck.
Coolsculpting, when done properly, is an incredibly safe cosmetic procedure. Given how the applicators are positioned, it is not likely to have any affect on a fibroid within your cervical region.