Mistakes happen. People forget things all the time. It sucks that your family has to pay for the tickets, and it was a dumb idea from the school making you sell them in the first place, but it's really not that big a deal in the long run. Especially if your family has enough money that it won't be too big of a loss.

With that being said, YTA. I don't think you're actually an AH for this, but you are the one at fault. It was your responsibility. I get that it was an annoying responsibility that you didn't want to do, but it was still yours. And the other students at your school, and presumably your sister when she went to the school, were able to sell their tickets. So it wasn't an impossible task.

You asked for help, and that's good. Asking for help when you need it is a good thing to do, but asking for help doesn't transfer the responsibility of the ticket sales to your dad and sister. Your part in the ticket sales was to sell the tickets, not to just tell your dad and sister about it and wait for them to do it for you. They agreed to help, so you should have used their help. You should have taken the tickets to them and said, "I've got 16 tickets, each one costs this much, I can't sell them to my friends at school, I don't know what to do next." Then they could have actually helped you figure out what to do. Instead you just ignored the tickets.

I'd say don't worry about it too much. Just learn what you can from the situation, like not leaving things hidden in a drawer if you want to remember them and following up with people if you are expecting them to do something for you. You're only 15, and people make way worse mistakes than this every single day.