To avoid the balance going to collections contact the hospital and work with them to establish a payment plan that is reasonable for your budget and is acceptable to the hospital. While I understand the desire to avoid bankruptcy, you should at least have a consultation with a bankruptcy attorney so that you know the options available to you.
Your options are to either work out a payment plan with the medical providers that is acceptable to them and realistically feasible for you; or consider filing for bankruptcy protection, which, depending on the amount of the debt may well be the most sound decision; barring either of these two options, the debt will likely go to collection and they can get a judgment against you and attempt to enforce that judgment. I understand that nobody wants to file for bankruptcy, but you should definitely not rule it out as an option. Try thinking of it as a business decision (take the emotion out of it just like a business would) and ask yourself if this is a debt you can pay off and continue to live at an acceptable standard, or will it sap much or most of your savings and income to pay this off...if the latter, then it's bad business to do so if you are eligible for bankruptcy relief.
I am located near you in McLean and would be happy to sit down with you for a free hour consultation to explore your options further.
Hospitals are aggressive collectors. They also will work with uninsured people to reduce payments. I suggest you contact them and find out what they need to consider this. Of course, three weeks in the hospital has made a huge bill, and even a reduced price may be impossible at your age and income.
Bankruptcy could well be an option. Yes, your credit score would take a temporary hit, but it will rise again after a short period, and it will help your peace of mind. This is not a debt you intended to incur, and bankruptcy does not say anything negative about you as people.
I'm located in Herndon and would also be happy to talk with you.