The Psychiatrist said No.
He is a medical Doctor....
his sleep problems could be for any reason which you do not know, the reason. It could even be stress or other school/home factors.
Regardless... if you give it to him, without knowing why.... then that is like "experimenting' on your own son. It would be guess work.
That is not good.
Or, if your son is on other medications for his ADHD... then anything else you give him, could possible cause more problems or maybe his ADHD medications are affecting his sleep, too.
You do NOT know that.