I am not certain who the debt collector is but I will assume it is the hospital you are making the payments to.  When you are making payments, there still is a balance outstanding with the hospital.  If the payments you are making are an equal amount each month, they should include an interest portion and a repayment of principal portion (this is called amortization).  Alternatively, the hospital might be charging you interest separately based on the outstanding balance you have each month because your payments are different each month.  To answer your question, the hospital is entitled to charge you interest on the outstanding balance owed to them each month.  You want to make sure there is not an interest component in your monthly payment AND you are being charged interest on top of that (double interest).

Finally, hospitals are willing to negotiate the amount owed, interest rate charged, etc., in order to improve their chances of getting paid something on the work that was done.  I would suggest that if you have not negotiated with the hospital on the total amount owing and the interest rate, that you do so as soon as possible.