Your sensor is an absolute pressure sensor, it is not suitable for differential pressure measurement. You need a differential pressure sensor.
Take a look at the MPXV7002DP, Farnell part 2080499. Not only is it differential, but it has a full-scale range of ±2kPa, which is near perfect.
Hint: DO NOT bend the surface mount pins to fit through a prototype board, these sensors have the chip mounted to the lead frame and any deformation of the leads will put strain on the sensor bridge, leading to horrible and unpredictable offsets. Instead, mount it to a PCB with the correct footprint, or loop tinned copper wire through the prototype board at positions corresponding to the sensor lead ends, then carefully solder the sensor down without deforming the leads. 