Do Not Make Little of Your Injuries

The immediate flow of adrenalin has the biological purpose of getting you out of harm's way. It will aid you in extracting yourself from an emergency situation and assisting others who are injured, setting up warnings for other drivers, and other accident-scene activities. It will do nothing to help you make a calm and reasonable assessment of what caused your situation or how to proceed logically. A final thing about the adrenalin rush is that it will likely disguise many symptoms of injury - including, specifically, the experience of pain. That is one reason it is important not to dismiss or make light of your injuries at an accident scene.
There is also a natural tendency, at least in our society, to make little of the circumstance and get ourselves and others back on our way. This is the result of embarrassment. For some reason, we are embarrassed about being in the accident and causing traffic or store customers to stop, delaying our friends or family who were on their way somewhere with us.
Do not make little of anything at an accident or injury scene. We have seen a great many reports from accident scenes where an injured person has popped up after slipping down and said she was not hurt, or where she suffered an injury from an auto accident but denied any injury. She said that she knew she was hurt because she felt some pain, but it was just a little pain. She was sure it would go away, so she told the police and others that she was not injured. Her pain persisted, and she finally saw the doctor six weeks later. The insurance adjuster would not pay full value, challenging the connection between the accident and her pains - based upon her own statements that she was not injured. You do not have to appear a heroic stoic!
That doesn't mean you should become an accident opportunist, be greedy, or that you should exaggerate your injuries. That behavior is even worse than denying an injury. It will diminish the value of your claim. Instead, give a realistic assessment of your injuries. If you don't know, say "I don't know. I'm too shaken by the accident to know anything right now."
If your injuries are obvious, there is no problem about reporting them. With soft tissue injuries, if you feel pain, you may talk about it only with the police, not with the other party. With soft tissue injuries, it is unlikely (but not impossible) that you are going to feel excruciating pain immediately. You can report that you feel an ache in your neck or back without getting too detailed.