Can moving a sprained ankle make it worse?

Minimal pain? Yes: Motion around a minimal to moderately sprained ankle is recommended. It is not recommended however in light of a complete ligament rupture.

Ankle Sprain: Ankle sprains are very common injuries. There's a good chance that while playing as a child or stepping on an uneven surface as an adult you sprained your ankle--some 25,000 people do it every day.​ http://www.aofas.org/footcaremd/how-to/foot-injury/pages/how%20to%20care%20for%20a%20sprained%20ankle.aspx