2003 Honda Civic Engine noise

When I first start the car as well as when I press the accelerator pedal, the sound of valves pumping is very loud and evident. It almost sounds like what you'ld expect to hear out of the engine on a model t. When driving, the sound is barely evident if the accelorator pedal is barely pressed. Any more pressure then that and you can hear it. I just had my oil changed with a synthetic blend as well as adding a Lucas oil additive. I also filled the gas tank with 92 octane as well as a fuel system cleaner but the noise is still there and seems to be getting a bit worse as the days go on.