Before you try anything more drastic, try replacing the battery. There have been many reports in this forum of Note 4 batteries going bad much sooner than might be expected. If you do replace the battery, make sure that you get a brand name battery from a reputable source, as there are many counterfeit Samsung batteries out there.
I have not seen your exact problem reported here before, but there are many reports such as "when I take a picture my phone shuts off" or "when my battery gets to xx% it suddenly goes to 0% and shuts off". And from my reading here (I have not personally experienced any of these problems) those problems were almost always resolved by a new battery. Some have even been able to get their carrier to replace the battery under warranty.
Larry