Hi~ You don't need a sleep study. They are quite costly and won't work if you can't sleep !
Speak to your doctor about a taper plan to wean you off the pills. At the same time,you can discuss your anxiety issues. You should only stop the sleeping pills under a doctor's supervision.
You should consult your GP immediately fairy, they will advise another medications that'll solve both the sleep issue and the anxiety and be sure to let them know these problems too.
talk to your doctor. He can wean you off and also try other medications that are not as addicting/you rely on them to sleep. Have you tried Valerian Root or Melatonin? Sleepy time tea? a hot bath before bedtime, dark room, and no noise. Some people just have sleeping disorders. Maybe you should try a sleep study?