In New York, you're required to have uninsured motorist coverage
, so you would be filing a claim under that coverage for your medical expenses. However, there isn't a legal requirement for the uninsured motorist property damage coverage - which you would use to file a claim for the damage to your vehicle. I would check with your policy to see if you have this coverage. For your property damage, there is a deductible which your car insurance company would reimburse you for. If you don't have these coverages, your next option would be to file a collision
claim. Now, the tricky part about this you will be rated for an at-fault accident which can be costly. If this is the way you go, I would get an estimate for the repairs and see if the at-fault party can compensate you for it. This way, you're able to avoid filing a claim and being rated for an at-fault accident. Either way, I would contact your insurance company's claims department and get their advice - at least for the uninsured medical claims.