Help making LEDs blink like blinkers in a car
It looks like you need to do something like:

if ((buttonStateRight == HIGH) &amp;&amp; (buttonStateLeft == HIGH)) {
    digitalWrite(ledPinRight, HIGH); 
    digitalWrite(ledPinLeft, HIGH); 
}
else if (buttonStateRight == HIGH) {
    digitalWrite(ledPinRight, HIGH); 
}
else if (buttonStateLeft == HIGH) {
    digitalWrite(ledPinleft, HIGH); 
}
//One delay for all
delay(500);
//Shut anything off that might be on after the delay
digitalWrite(ledPinRight, LOW); 
digitalWrite(ledPinLeft, LOW); 


Your code is really hard to read but it may mostly be because you need to insert four spaces at the beginning of each line of code to make it look right on this forum.