When we get embarrassed our body releases adrenaline. This will tell our heart to start beating faster and our blood vessels to become bigger so that more oxygen can travel through our bodies. Our facial skin has more and larger blood vessels that are nearer the surface of the skin, which make the changes in our blood circulation more obvious in our face when we get embarrassed.
People also blush when they get scared because adrenaline is also released then and the same reaction takes place. Have you ever noticed that you blush when you are scared……??? BOO!