Why do my superficial temporal artery and the arteries around my neck pulsate fast when lie down on the side of my head? is it a problem with my spine

The superficial: temporal artery travels near the zygomatic arch, the prominent part of the facial bones in your upper cheek. Because of being near a firm structure, it is easier to see/feel. I doubt that lying down is actually making your heart beat faster, but the rapid rate is more observable. Stress/anxiety could be causing rapid beating, but it dserves a good eval with your doctor. Doubt it is your spine.