I hope all is well. Usually, in New York State, a tenant owes no obligation on a lease agreement until the lease is fully executed by landlord and tenant, and a fully signed copy of the lease and keys are given to the tenant.
If this is a for a dormitory room there may be other conditions which apply only to rooms in a dormitory. If the lease is for student housing there may be other rules.
For a better opinion, show the lease to a lawyer.
Based upon your stated facts, the lease process is not complete.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.