In all the material realm sin is an attribute only of humans. This is because no other physical entities can know right from wrong. All things other than people do only what God has given them an instinct and ability to do. What they do may not suit what we think they should do. However, since they do not choose their actions based on knowledge of right and wrong, they are free from guilt. I believe that this was true of the first-creation humanity before the later version came to know right from wrong and hence to be able to make sinful choices.
The new type of humanity came to know right from wrong by doing wrong. You know the story and it seems only fair to credit both Adam and Eve for this addition to human capabilities. However, we should note that their punishments differed. Adam, I believe, bore the guilt that has been transmitted to all his descendants. This guilt could not be transmitted through Eve because a woman was to bear the child that would offer all humanity redemption from our guilt.