Who is liable for medical bills if I rear-ended another car?

Question Details: I was involved in an auto accident in which I reared-ended someone. He agreed not to call police and let me pay for minor bumper damages. He said everyone appeared fine. It was him, his daughter in front seat and his other daughter in back seat. He said he would email me the next day, Saturday, if anyone was needing to see a doctor. He did not email me. Instead he emailed me Tuesday, 4 days later, to say his daughter was dizzy and had a headache that night, the daughter in the back seat. She went to the doctor on Monday and they said possible concussion and would be out of school until they did a concussion test. I have no damage, just scratches. His damage is a small debt on right side of bumper with some scratches. Am I responsible for his daughter's medical bills? Now he wants to go through my insurance. How do I know she hasn't been injured in the days after the accident and since he didn't let me know the next day she had symptoms?

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