I don't know where you are getting your info from but the New York city airports were shut down Monday and early for Tuesday. Even when the airports did open back up they have to get the planes there and not all are going to make it. Also in case you didn't realize it you were not the only person trying to call. There was probably such a backlog of calls that they couldn't take anymore. They also probably had their reservations folks buys rebooking people.
The mis booking was squarely their fault, but you travel agent should have been able to still make the change. You need to talk to your travel agent on that part.
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