Mmm, well it looks to me like a genuine Group ticket you have, poor you! It would not totally surprise me if you can't check in online, but I certainly hope you can. Normally going to the airport a day beforehand won't help, I think that stopped being useful sometime in the mid 1990s, though perhaps if there was one outstation where they would it could be Kennedy. However in this (fairly dire!) situation I'd turn up at T7 a good 3 hours beforehand smelling sweetly and hope the beautiful (etc) agent can find an AUP for me, offering to go on an earlier service if it helps and so on. Good luck, and I suspect you will need it. I'm afraid this is a case of you get what someone else paid for.