I understand that Adam and Eve sinned, but why should I get punished?
Yes, that can be confusing. I did not eat the fruit off that tree, why should I be part of the blame? I was not even born. You need to see mankind as God does. Let’s take football. When a player on the line crosses over that line before the football is hut, it’s called offside and the penalty is 5 yards back. The referee does not send the player that committed the penalty back 5 yards but the whole team. The referee does not look at the one player but the team as one unit. God does the same thing, he looks at mankind as one unit that sinned when Adam and Eve ate the fruit.
Therefore, just as sin entered the world through one man (Adam), and death through sin, and in this way death came to all men, because all sinned.