I was prescribed melatonin when I was 11. In the UK it is only available via prescription (source on that: https://www.simpleonlinepharmacy.co.uk/health-advice/sleep/melatonin/why-is-melatonin-banned-in-the-uk/#article )
My sleep schedule was haywire (hormones + emerging gender dysphoria did not help) but melatonin really helped me. I also think it helped my anxiety a bit? I’m not sure if that was just bc I was sleeping better but I have terrible social anxiety and it seemed to take the edge off it. anyone else? :)
There are brands that sell melatonine that will start working after some time. My son gets a blend of fast and slow release melatonin, as he had the problem you describe: fall asleep somewhat normally and be wide awake in the middle of the night.