Sounds like your temp sensor/control unit is on its way out. The T&P relief valve on the water heater is intended to protect you in a "runaway" firing scenario. You may want to check it by "popping" it open to make sre it's not rusted closed. This manual popping is recommended as routine maintenance.
For absolute safety, you can turn to WH control to the "pilot" position, in which case it will not fire to heat water. Wake up an hour early tomorrow, turn it back to the "on" position, take showers while monitoring HW temp, then return to "pilot".