If the debt has been sold to a collector and you have verification of this, send the money to the collection group. If the hospital no longer holds the debt, it would have no way to credit the payment to the account. Make sure you maintain excellent records about payments, dates, amounts and the address to which it was sent.
Talk to someone at the hospital first, but most likely to the debt collector. Make sure you keep detailed records of your payments to the debt collector though, as it's possible for the debt agency to go out of business or stop sending payments on your behalf to the hospital.
If the hospital has put the bill into collections then you have to send the money to the debt collector, they will not be able to accept the money. Make sure you keep the name of the person you deal with at the collection agency and keep receipts or confirmation numbers of your payments.
You should send the money to the debt collector. If the money that was due has been turned over to colletions then they will distribute the money to the hospital.
You should send your money to the hospital directly if your debts weren't sent to a collection agency but if the agency has your debts, you should mail to them.