Rear Ended Someone- No Damage/no Police Report. Trying To Claim Bodily Injury

Hello, on Saturday Jan 28th I was helping my friend move. I was alone in my car and approached a stop and went to reach for something and rolled. I rear ended the person in front of me but luckily there was no damage to my car or the other car. We pulled off about a quarter mile away to look, exchange info, and exchange insurance. No police report was made and we were off with in minutes. He now is trying to say he has stiffness and soreness and is wanting to make a claim. Does he have any case here considering there is no damage and no police report made? It has also been 3 days since this happened, curious if there is some kind of time limit on doing anything. I live in Washington state if this makes a difference.

I also find it somewhat odd, he has texted me to ask if I feel hurt, cause he definitely does. And when I tell him I’m fine, he tells me he’s definitely hurt so he’s thinking about filing a claim. Idk if this is him trying to be nice and give a heads up? But somewhat comes off threatening. I have made sure to not apologize for anything over text since I know that can show I’m taking fault.