This is what uninsured/underinsured covereage is for. The UM coverage on your own auto policy should cover this completely, meaning medical bills (8 hours in the ER is pretty pricey) that are not covered by PIP (try not to get your own health insurance involved - they will have a lien against any other recovery, so what they pay gets taken from other insurance recovery), wage loss (taking sick time counts as lost wages), property damage, and possibly other damages depending on NY law. If the other driver an be identified, he might be held responsible, but that for the insurance subrogation department to worry about.