Hypnosis isn't quick like that -- it takes a long time, like any therapy. I did it and liked it, but it didn't work for my panic attacks. There are no guarantees. But the person I saw had expertise in hypnosis. Keep in mind that most psychiatrists, especially those seen through health plans, don't do therapy, they just dispense drugs (and they often know very little about those). If they do therapy, they're quite expensive, so it's cheaper to get therapy from a psychologist, and then you have to find one whose expertise is hypnosis. And it isn't going to work like magic, it's still you they're working with. The main purpose of hypnosis is to get you to relax so you're more open, it doesn't work like in the movies.
Well unless your Psychiatrist does Hypnosis, it would be like walking into your dentist and asking him to do it. I would not demand something unless your sure your Dr. does it.
Also it really does not work that way, any sugestion you get from your Dr. would have to be something you want and your MIND wants, Anxiety has to do with ISSUES, so if you have not worked on issues, it will not work.