Definitely appeal it. You've paid for the second ticket and I would think that you can use that as evidence that you got a ticket and paid it.
Incidentally, if you ever go back to your car and see a warden writing you a ticket, don;t speak to them, just get in and drive off as quickly as possible. The ticket is not issued until they place it in the waterproof see-through wallet and stick it to your window. If they haven't done this, you haven't been given a ticket yet. (I learned this one the hard way but I'm dying to do it next time)