is it possible to get a loan like this without a cosigner?
If your parents apply for the Plus Loan and are denied the loan...then YOU would be eligible for additional Stafford loan money, I believe, in your name, but I'm not sure of the amount.
In any event...it sounds like you cannot pay the bills at NYU. Your family doesn't have the resources to do so. Truthfully, I don't think applying ED (on a wish that the money would come) was such a good idea, but that is water over the dam. The reality is your financial aid package does not make it possible for you to attend.