LOOK_UP and LOOK_DOWN must rotate around the x-axis, not around the y-axis.
ROTATE_RIGHT and ROTATE_LEFT must rotate around the y-axis, not around the x-axis.
Immediately rotating around 90 degrees or initializing your angles with 90 degrees will bring your system into a Gimbal Lock state, resulting in weird rotations. You might want to use smaller angles and step-sizes for starters, particulary not 90 degrees or multiples of it.
Initialize all angles with 0 and start from there:
// init your angles at startup, i.e. main or camera constructor
player.camera.rotation.x = 0.0;
player.camera.rotation.y = 0.0;
player.camera.rotation.z = 0.0;
// change the step-size and rotation-axis like this:
case LOOK_UP:
player.camera.rotation.x+=5.0;
break;
case ROTATE_LEFT:
player.camera.rotation.y-=5.0;
break;
case LOOK_DOWN:
player.camera.rotation.x-=5.0;
break;
case ROTATE_RIGHT:
player.camera.rotation.y+=5.0;
break;