Simply put, Panama, like most of Central America does not yet have a life flight type service. You are basically on your own with limited support from the government, which does have some capability. However, they have increasing responsibilities on the border with Colombia making air asset availability less than reliable. This means that you must look for other means to get back to Panama City if the local health care facility cannot treat you, which is highly likely outside of David where there are two private hospitals.

The snag is that medical specialists live and work in Panama City and rarely venture out to David. Their largest market is in the nation's largest city.

Do not assume that your health insurance or credit card policy will cover you either. 

Here are some examples of private medical charter flight costs:

Bocas or David = $4,000 plus

San Blas = $2,000 plus

Pedasi = $1,400 plus

This includes the cost of the plane, flight paramedic and medical supplies.  

Private charter companies will require a credit card, wire transfer, or cash upfront for payment. 

There is one inexpensive alternative so use your favorite search engine and look for air medical transport panama.

 If you fly into Tocumen, then be sure to pick up your tourist medical coverage information package. Panama now offers 30 days worth of coverage for visitors. It includes air medical transport coverage.