Who's auto insurance is responsible for medical if the other driver does not have insurance?

This is a no brainer ... if the other driver has no insurance, how possibly could their non-existent insurance be responsible for medical? The only recourse here is to take the other driver to court and sue for damages. Chances are you will still get nothing - most likely if someone cannot afford auto insurance, they certainly could not afford any out of pocket medical expenses.

This is why most motorists have to carry under-insured and un-insured auto insurance on their policies ... for your own protection.