Why is my car making a grinding noise and rpms jumping at the same tim

"I am not a transmission expert but I have been working on vehicles since I was old enough to hand my dad a wrench - 30 + years ago.

This sounds like your transmission is going out. Primarily 2nd and 3rd gear. Your gears are not fully seating, the gear that slides on a shaft between 2nd and 3rd that is. Your transmission will need to be rebuilt since metal shavings will ruin the trans lubricating system. The grinding is because the shift from 2nd to 3rd is not fully happening. The increase in RPMs is since the gears do not fully engage the power gear free spins based on motor RPM. With you having the gas pedal pressed for acceleration there is no resistance from gear shifting to keep the motor from obtaining high RPMs.

Sorry"