I was in a car accident last week where I was hit from behind, the driver who hit me was cited and in the accident report he stated"he hit me dead on"

The other driver is obviously at fault, and the accident happened in a Fault State (Ohio), but my insurance policy is in New York which is a no-fault state. So, even though I am not at fault - my insurance company wants to pay my medical bills and lost wages and I have to file a claim with the other drivers insurance company to fix my car, but it seems I am not entitled to seek compensation for my injuries ( I have pretty bad whiplash, I have to have 6 weeks of chiropractic/physical therapy) and I was prescribed muscle relaxers and pain medication. Is this correct? Or since the other driver is at fault in a fault state can I go after the other driver''s insurance company regardless of my no fault policy? My insurance company sent me a check for lost wages, I don''t want to cash it until I get this question answered.