Is the questioner considered sinful for involuntarily hearing music, despite her intense dislike for it and her futile attempts to change the channel?

Allah Almighty does not hold a servant accountable for what they are coerced into, as long as their heart is firm in faith; as Allah the Almighty says: (Whoever disbelieves in Allah after his belief, except him who is compelled thereto, and his heart is at rest with faith). So, as long as you dislike hearing music and do not listen to it, there is no sin upon you. You should resist this corruption and distance yourself from it as much as possible. If you are unable to do so, there is no blame on you as long as you dislike it.