NYU defines need Acc to their own institutional formula which is not likely to match up with need defined by FAFSA EFC. Then, on top of thst, they do not guarantee to fully meet that need as they define it. From what I’ve seen, any merit awards and scholarships reduce financial need, soon your case it appears as though that Gallatin specific scholarship reduced any financial aid that they may have had available for you. As a private school, they can do as they please.
If you are PELL eligible, you should be able to get the PELL grant from the feeders government. You can also borrow up to $6k as a sophomore, some of it likely with subsidized interest if your FAFSA EFC allows it with the scholarship factored into the equation.
Most all of the schools that state they meet need fully, do so according to their own formulas and many do not include Transfer students in that guarantee.
When your other acceptances and aid/merit packages arrive, you and your parents should assess the affordability of each school. Yes, you can discuss the aid packages with the school financial aid packages and appeal for more. However, in my experience, my observation that it’s rare that one gets substantially more in grant money. Though it can happen, I advise you to focus on the affordable options as reality and not count on getting what you need from packages that come short. Unless your parents are in good financial shape and willing to make up any gaps, it’s not a good idea most of the time to push them to borrow the gap. Unlikely , you, the student can borrow enough to make up a large chasm.