You could have a defective battery. Apple has a [https://www.apple.com/support/iphone6s-unexpectedshutdown/|recall program] for the iPhone 6S experiencing unexpected shutdowns. I would check out the site to see if your phone is eligible for a free replacement.
You say and iTunes enabled computer does not recognize the phone. Do you use non-original chargers to charge your device, like a cheap car charger or fake Apple charging brick? Those are known to blow out the charge circuit on the logic board.
You should also consider sending your phone to a reputable micro-soldering repair shop. They will be able to properly troubleshoot your device because it sounds like you have a logic board issue (check the battery first).