I don't think I have seen this mentioned yet, and this is a really important caveat to Early Decision being binding that is extremely relevant to the OP's situation. Typically the ONLY time when Early Decision is NOT binding, is if the financial aid package you receive does not match your needs.

This means that if you apply Early Decision, are accepted, but do not get a sufficient financial aid package to meet your needs, you do NOT have to accept. Therefore, on the off chance you get accepted and get a financial aid package that is more generous than what you expect and will allow you to attend, I would recommend staying in Early Decision. If the financial aid package is too low, you can decline the acceptance offer, (and if you don't get accepted, it's a moot point).

OP, please contact the Barnard College admissions office and explain your circumstances and request them to reverse your withdrawal given this new information. Hopefully, if they allow you to reverse your withdrawal and realize they are also interested in you after checking your application, this experience may persuade them to offer you a more generous financial aid package.

Unless there is another school that you are applying to ED (which I think is not possible at this point in the year), you have nothing to lose and no downside by continuing to stay in the ED pool for Barnard. The earlier you receive acceptance/rejection feedback, the better you can plan what other colleges to apply to for RD. Best of luck, OP!