An emergency appeal from NY (2nd Circuit) would go to Justice Sotomayor. She has the option of denying the appeal herself, or allowing the full court a vote to allow or deny. IMHO, she is likely to deny the appeal and allow the appeal process to progress through NY Appellate and NY Appeals courts.
If the circuit justice denies, you are allowed to go to any other justice. That’s why when it’s questionable the justice will go ahead and submit the matter to the full Court (along with a personal recommendation, which we never see).