outside ankle strain

I just realized I supinate, but the only problem with that is outside of ankle behind ankle bone hurts after only an hour of walking, been a problem for years, I have always been a walker, jogger, but for some reason it shortens my workouts due to this strain on side of ankle, I noticed when I walk my ankle turns in or heel I should say slightly turns in ward bowing out the outside of ankle,(like a partial spraining movement)and I do notice a jarring affect when I walk, probably due to the supination, and mild high arches,anyway I was wondering how to support my ankles to avoid the bowing affect which is straining that ligament on the outside of ankle, because if I could stop the strain and subsequent pain I can walk for hours and even hike for hours, it is that ligament on outside of ankle that ends my workouts way before I am tired. what kind of ankle brace would stop the inversion of my heel (rest of my feet seldom bother me except after at least two hours of hiking trails)without straining other ligaments in my ankles and lower leg when I hike? you know without changing the stressors on my lower limbs causing other parts to start to hurt?
thanks. oh forgot that pain goes away within a day or two when I rest. but it repeats once I walk for more than an hour.RR