How long after a car accident can you claim injury?

I told the cop and the other driver I was fine, waved off the ambulance, didn't mention pain because there wasn't any yet. That was the night of about ten days later my neck and right shoulder started locking up and I've had these low grade headaches that won't quit, and now I'm reading that delayed symptoms are a whole thing after a crash and I just sat on it.

So how long after a car accident can you claim injury if it didn't show up at the scene? I never signed anything with their insurer, never gave a statement, the only record is the police report that basically says nobody was hurt. Is a delayed injury claim like this still possible, or did I quietly wreck it by saying I was okay when I genuinely thought I was?

I'm not trying to invent an injury. This is real and it's messing with how I sleep. I just don't know if waiting almost two weeks to connect it to the crash means they get to wave it away. Anybody dealt with the symptoms showed up later version of this?