No doctor from online (WITHOUT EXAMINING child) can overrule/ supercede the written advise of the doctor who has examined the child: hope that this is very clear.
is there any side effect of CT scan head? Yes, most important being radiation, sedation (to prevent movement of head)
But as always, any test/investigation is all about risks versus benefits
Next Steps
As you yourself mentioned that the cut is deep, CT brain especially with bone window focused on the site of cut is helpful in deciding whether there is any underlying bony fracture/involvement