I've not used Arnica on sprains but had all 4 wisdom teeth taken out (under general anaesthetic) as a teenager and was fed arnica orally on an hourly basis by my mum for the next 2 days and was told by the doc that I healed very quickly. Some swelling but down pretty fast and back to normal in less than a week. My sister had exactly the same thing done with the same treatment and she also healed very quick. No bad side effects for either of us. Of course we were both young fit and healthy and maybe we just healed quickly anyhow. My mum used the same treatment on herself post abdominal surgery and also seemed to heal fast. (NB I've a science background and suffer the same mix of scepticism and surety that modern science doesn't know all the answers).