My doctor told me CoolSculpting was ok to do while I'm breastfeeding.

We
do not recommend that anyone who is pregnant or nursing have
CoolSculpting or any other medically unnecessary procedure. This is
not because we know it to be harmful but because the medical
profession prefers to err on the side of caution – particularly
when it comes to developing or newborn babies. There are no studies
on the effects of CoolSculpting on expectant or nursing mothers –
nor will there ever be. It wouldn't be ethical to test a cosmetic
procedure on this population. But please don't worry! This is a
wonderful time of your life and you should enjoy it without the
stress of feeling like you made a mistake. There is also data that
breast feeding can not only help your baby, but mobilize and help get
rid of fat in stubborn areas of your body, so it is probably helping
to get rid of pregnancy fat! Please find a board-certified
dermatologist to help you the next time you want a cosmetic procedure
to be sure you get the best and most complete care. 

Thank you for your question. Coolsculpting should NOT be done when pregnant or breastfeeding. The treatment has not been not tested on pregnant or breastfeeding women, I strongly advise against treatment at this time. Regards,

CoolSculpting® hasn't been approved for use while pregnant or breastfeeding, so I would encourage you to wait until you've finished breastfeeding to continue with your treatments. If you have concerns about lactation or your baby's health, discuss these with your pediatrician. 

For the future, keep in mind, too, that right after pregnancy and while you're breastfeeding, hormone fluctuations within your body can have a significant effect on your weight. Because of this, you're going to get better results anyway once you've reached a stable weight after your hormone levels have normalized.

You should wait till your done breastfeeding . After pregnancy your uterus has enlarged and will take time to reduce in size, you have hormonal changes that haven't stabilized and your abdominal musculature will change.
If you are concerned about the treatment having determental effects on lactation for your baby, no one knows the answer because the treatment has not been tested on pregnant or lactating women and probably never will. Retrospective studies may eventually be done but at this time there are no recommendations except to avoid treatment and to err on the side of safety.  Basic intuition would suggest cold exposure should not have determiental effects but there is no way to accurately answer this issue at the present time.