If you owe someone money from several transactions (e.g. from several different bills or invoices; for services provided at different times; etc.), it is up to the creditor which bills to apply payments to. The creditor (the hospital, in this case) gets to decide which debts to apply your payments to; you do not get to tell them which debts they need to pay off, in which order (though sometimes, as a courtesy, a creditor will apply payments per the debtor's instructions; however, this is a voluntary curtosy, not an obligation). It is actually very common, as well as legal, for creditors to apply payments ostensibly made to newer debtrs or for newer bills to older bills, to clean up the oldest debts first.