This is just me speaking from personal experience. I'm not a doctor or anything.

Typically doctors are pretty hesitant to prescribe hypnotics, especially to teens just because of their risk of dependency or abuse. Your doctor will probably talk to you about healthy sleeping habits and all that. The first time I went to my doctor to talk about sleep they recommended things like melatonin and teas, which did absolutely nothing for me. Haha. They might recommend an anti-anxiety med at a low dose like Xanax or Klonopin because they can have sedating effects. And for a lot of people that does the trick.
I highly doubt they'll suggest anything like Ambien, which is pretty much a last resort sleep medication.
As for what's best for you, only you can really know that. Sometimes it takes a while to find what works best, but if you work with your doctor I'm sure y'all will figure something out.
If you want someone to talk to who has gone through/is going through a similar sleep predicament, feel free to message me.