Yes, Ambien can be addictive. It was my favorite DOC to mix with alcohol when I was practicing -- thank God I'm still alive!
I have used it in sobriety, but be careful -- it's very tempting to make it a long term habit.
The safer way I think would be a natural supplement. Try Sleepy Time tea or Melatonin. I take Melatonin pretty much every night. Doesn't make you drowsy or anything, but once you fall asleep -- you're asleep! Also, maybe try some relaxation techniques...
Good luck, sleeping will come easier in time!