You need a function to shut off the alarm when you release the button.
However, the way you've debounced your button is confusing. There's no need for a lastButtonPushed variable, just test the state of the button itself, like this:
if (lastButtonEnterState == LOW){
AlarmTest();
}
else {
lastButtonPushed =0;
digitalWrite( buzzerPin, LOW ); // <== Turns off buzzer when the button is off.
}