My psychiatrist has discussed the older model of this drug, gabapentin, or Neurontin. That's cheaper and probably works as well, but for anxiety it's usually used as an augmentation to an ssri or something rather than as a primary med. It is used as a primary med when you have something intractible and they start throwing the kitchen sink at a problem, which is, unfortunately, my case, but not yours. I would see a psychiatrist rather than a neurologist for anxiety, and probably, if it isn't crippling you, try therapy before that, as meds will help the symptoms but won't solve the problem. Good luck whatever you try.
While pregabalin, known as "Lyrica" in the States, has unlabeled uses for GAD and SAD, (Generalized Anxiety Disorder and Social Anxiety Disorder) it is primarily prescribed here for fibromyalgia and neuropathic pain associated with peripheral neuropathy. Nowhere can I find that it is beneficial for sleep problems, although one of it's side effects IS "fatigue," I don't think that is the desired effect for a sleep aid.
I am not a doctor nor a pharmacist, but if it was ME, I would definitely discuss with my doctor his choice of this particular med. There are many drugs on the market that target GAD and SAD specifically. Just my opinion.