Am I sinful for changing the channel to a song at the request of my relative, and then leaving the place?

The ruling differs according to the nature of the song. If it is permissible, there is no sin upon you. However, if it is forbidden or accompanied by something forbidden, then you have erred, because this falls under the category of assisting in sin. What was obligatory upon you was to forbid and prevent it. It is forbidden for a woman to seclude herself with any man who is not her mahram.