My hypothesis about the Evolution of Morality

Here is my explanation of morality, which I believe is a slight variant of Dawkins' selfish gene explanation of altruism:

Studies have shown that when you see someone else in pain, your brain responds as if it were in pain*. You see someone in pain, and it reminds you of your pain, and your brain reacts accordingly. In a situation where you are near them, you will react to try and relieve their pain (to relieve your own). I hypothesize that this is either a byproduct of the brain and of remembrance which just happens to be beneficial was not altered, or that it evolved by a selective advantage for groups with at least one altruistic individual (having at least one who rescues others from pain or death is still advantageous).