I would record it.
The exact club form may vary, but an injury record should capture the facts: what happened, when and where it happened, what immediate first aid was provided, who was informed and who the player left with.
Keep it factual rather than diagnosing the injury.
That record can matter if symptoms change later, if the club needs to review a safety issue or if the same incident is remembered differently by different people.
I would also make sure the club, not individual coaches, owns the storage process because injury information is sensitive personal data.
The best time to decide how injuries are recorded is not after somebody has been hurt.
Have a standard form or digital process, identify who completes it and know where it goes.
For a minor bump, the record may be brief. For anything significant, good notes protect the player and the adults involved.