Is your condition stable, slowly worsening, or critical?

Before you do anything, talk to your doctor. They might be able to recommend a specialist in-state or closer than NY. They may even be able to work with a doctor in another hospital. If you want to go to NY, talk to the hospital directly (not through your cousin) and buy the ticket as close as possible. Unless your condition is severe and worsening, they may not be able to take you in immediately. Look at the hospital online and see if they have telemedicine services. You might be able to make an appointment through that.

Lastly, for the incoming medical bills my advice is this:

• See if you qualify for financial aid through the hospital.
• Get an itemized bill and ask if there’s anything that can be reduced.
• Get the lowest payment plan that you can. Never miss a payment. After some time you might be able to pay it off a reduced bill or it may even be forgiven.