Can a collection agency report medical debt on my credit report?

How much do you owe? Usually, hospitals send medical bills to collections after 180 days, and that is when they can report to the credit bureau. I would suggest you to negotiate before the hospital bills are sent to the CA.

Try to find out the hospital address or phone numbers from the bill and talk to the hospital regarding settling the debts. Try to negotiate and reduce the bill. If they agree, repay the amount within the said time. Try to settle the debt with a lump sum amount. If you are in financial hardship, you can go for installment payments as well. Make sure, you make the settlement agreement and keep the copy of the agreement.

How much do you owe to them as medical debts? Call them and discuss a repayment plan If you can able to pay them in full.
If you can't pay the bills fully, I would suggest you to take help from a debt management company and settle your debts.

If you can't do it on your own, you can always do it with professional help. So, if you feel it's not your cup of tea, then choose a good settlement or consolidation company for the purpose.
Whatever option you choose, opting for settlement can help you be debt free faster but you may have to pay a tax on the forgiven amount.
So, think and decide what you want to do.