Well, as a citizen of your country, you deserve the right to have your needs met. If painkillers help relieve the symptoms of this medical issue, then I can't see any reason why you should be denied a prescription. Not all medicines are prescribed to a single condition (painkillers for pain) and many serve multiple purposes. Though I would never recommend getting yourself addicted to opiates, though if it helps your condition and stops your suffering, then I can't really deny it either.
I have only suffered RLS during opiate withdrawal and it is a hellish feeling. I had it infrequently as a child but grew out of it, fortunately.
I'm afraid I can't help much as I have never really researched it much, though I thought I'd do a quick google search for you, which turned up this bit of info:
"Iron - Low iron in the brain can contribute to RLS, a diet high in iron can prevent symptoms.
Caffeine, tobacco and alcohol - All of these can increase and worsen the symptoms of RLS, so it is very important to avoid these substances.
Food - Some studies show that having reactive hypoglycemia can put you at risk for developing RLS. It is recommended that you eat several small meals and avoid high sugar foods while eating whole grains, nuts, seeds, fish, fresh fruits and vegetables.
Chiropractic care - Some chiropractors believe that a part of RLS is having pelvic instability. A chiropractor will recommend strengthening exercises for the pelvic area, consistent walking and leg stretching twice a day.
Acupuncture - Needles are placed at specific areas of the body to either stimulate or turn down certain nerves, when used in RLS, acupuncture can reduce symptoms in as little as one session.
Homeopathy - The guidance of an experienced homeopath is important and can often help to relieve symptoms.
Vitamins - Studies show that the use of specific vitamins and minerals like vitamin E, vitamin B12, magnesium, calcium, zinc and folic acid can help relieve the symptoms of RLS."
I wonder....have you tried wearing out your muscles with vigorous exercise? Do you think a steady, challenging resistance training program would help?