On ANY loan (except a prepaid interest/ Rule of 78th loans, and no federal loan uses that method), the terms of the loan are going to dictate the lender apply the payment to outstanding charges (late payment fees, bounced checks, etc), then to accrued interest, then to principal. Where people get confused is if they pay a double payment and then want to skip the next payment. For that you have to ask the lender for special processing or the double payment is going to be used to pay accrued interest and then an extra large payment to principal; when the next payment isn’t received the next month, interest will continue to accrue (and perhaps a late payment charge). If you have accrued interest, you cannot instruct the lender to apply a payment to principal first; the interest has to be paid first.
You have to decide if you want the money available for an emergency in your junior/senior year, but it is expensive to have money just sitting in the bank. I think if you have it you will spend it, whereas if you repay it and need more money in junior/senior year, you might find another way to get that money (work, spend less, sell some belongings).
The lender is required to follow the terms of the loan and apply payments as the terms require. The lender is NOT required to recalculate your payment schedule every time you make an extra payment to principal, but some will do it upon request if the principal is significantly decreased. In this case, the OP has no regular scheduled payment schedule yet, so when the loan goes into repayment status, the payments will be calculated based on the balance at the time repayment starts. Think about a 30 year mortgage - the bank is not going to change your payments if you make an extra payment once or twice per year, but you are going to pay off the loan years earlier by making extra payments. Each of those extra payments went to principal reduction because the outstanding interest was paid by the regularly scheduled payment that month. If the accrued interest is paid, there is no place to apply the extra payment except to principal.