Dbarlo, very frustrating, esp missing the 1 yr old's picture. But good news for you: every single user that came here and pursued resolution steps (diagnostics, Genius Bar or Sr Apple Support, Authorized Service Center) had their problem resolved. Over fourteen successfully resolved with battery replacement a few more had phone replacement. As you start this process, be mindful, however, of your battery age. If your 6 has over 500, 600 - or 1000 cycles like some do, all bets are off as the technical world sees it as done and why it would do this. If they recommend you a battery replacement, in that case, they are correct. If, however, you have a low cycle number, wait and see what Sr Advisors recommend. Other users, as myself, over the years fried iPhone with non-Apple cables. So variables are many. You might point out it started with iOS install, we know, as do all here whom resolved it. Bottom line is all these installations are stressful for batteries, and marginal batteries may fail calibration and firmware on such high demand cycle/install.
So you can have this thing resolved in hours or days, depends where you are and how quickly you determine the problem. You will also see people spending inordinate amount of time insulting Apple, and their issue is never resolved. Then, you have users whom resolve it. Time is important. Some are lucky with xtended warranty, or courtesy service from Apple, reverse authorization shipment, etc.