When it comes to getting more financial aid, determining who you need to speak to in a college makes all the difference.
Financial Aid offices primarily handled need-based aid that comes from filing a FAFSA and alternative loans. Perhaps some office directly oversees merit-based scholarships but that is not always the case. That scholarship you're being offered is most likely coming from another department. You may want to look into the following departments for additional scholarship/grants opportunities: the admissions office, your specific department chairman's office, your student government, your alumni services department (yep they can offer scholarships to new students sometimes or provide funding towards projects in some cases), and/or your resident's life/housing department. Different departments handle different budgets so while one may not be able to offer you something, another might. Also, you may not be eligible to apply in your freshmen year but perhaps in following years you become eligible.
Basically, Financial Aid offices may not be your direct/sole point of contact for internal merit-based aid. They should definitely be your first stop because we tend to offer databases for external outside scholarship opportunities and should point you to the departments listed above. One avenue Financial Aid offices should work with you on is processing a need-based appeal based on financial hardship. Reach out to your financial aid office at your school and ask what they need to get that process started. The FAFSA uses two years prior info so appealing from financial hardship allows the Financial Aid office to take in factors like employment change/loss, additional expenses, unforeseen circumstances, and/or health issues.
Lastly, some schools put a Federal Direct PLUS loan on your award letter. The PLUS loan is a credit-based loan which your parents (Parent PLUS) or a graduate student (Graduate PLUS) may be eligible for after you complete a FAFSA form. BUT the borrower MUST pass a credit check to get it. Don't be deceived into thinking you are fully covered by a PLUS loan if no one has actually applied for it yet.
Good luck funding your education everyone!!