Could the heater core have gone bad or the sensor as well?

First - MUST confirm floorboard is wet with ANTIFREEZE instead of water from clogged air conditioner drain tube! .. Antifreeze has a distinct smell - also taste sweet when touched to tongue with finger - if you want to go that far. Second - MUST confirm engine did indeed overheat and you’re not simply mistaken. Many reasons for blinking check engine light and other symptoms mentioned. In other words - *hands-on* evaluation by qualified personnel will be required here. Good luck!