We started using Melatonin for our 10 yr old, and the 3mg didn't work so we had to up the dosage. I would definitely consult with your physician on the correct doseage. The Dr said it's all natural and your body needs melatonin, but wow, 3 is pretty small. I'm sure you've already tried the lavendar nightime lotion, etc.
I would definitley ask your Doctor. Since we have upped the dosage to 4.5 mg it's been wonderful,and very successful, my daughter would be awake all hours of the night,sometime until 4am and then she would not sleep in, so she was averaging 4 hrs of sleep if we were lucky this past sumemr, and would be scared even if she did come into our bed, kids need sleep, if they don't get it, it can really cause bad effects. This is the first time my daughter actually asks to go to bed! It's been a lifesaver, but we also found out our daughter has anxiety, and many children do with sleeping issues, so we have also been working with a therapist to help with that. I would definitely speak to your doctor.
Good luck and the Melatonin has been a great help to us, but I would be cautious using it.
OH one onther thing, the Dr also said to get one of those sleep sound machines, like you can get a brookstone, he said not to listen to music, we had bought some of the relaxing music for her to listen to, but he highly recommended this machine and it's helped a ton too, Tranquil Moments® Sleep Sound Therapy System, you can buy online or at brookstone, just something else to try!