It is very common to lose range of motion after an ankle sprain because of swelling. The standard treatment for ligament injuries such as an ankle sprain include dynamic splinting (an ace bandage can work) as well as rest, ice, compression, and elevation.
Most emergency room and orthopedic doctors follow the Ottawa rules for ankle injuries (source: http://www.bmj.com/content/339/bmj.b2901.full).
For ankle injuries an X-ray is warranted if there is:
1) Any pain on palpation of the medial malleolus
2) Any pain on palpation of the lateral malleolus
3) Any inability to bear weight immediately after the injury or in the emergency room
These tests are very accurate any only miss about 1% of patients with ankle fractures. Although an emergency room visit is important for major ankle injuries, the choice is ultimately up to you to determine the severity of your injury. However, if you test positive for any of the above signs, it is important for you to go to emergency room immediately to be evaluated. Follow up with an orthopedic doctor is also recommended depending on the severity of the sprain as it is important to determine if you have severe ligament injury (such as a tear).
Therefore, although home remedies such as dynamic splinting, rest, ice, compression, and elevation can help, it is important to be evaluated in the emergency room if you have pain in the areas described by the Ottawa rules for ankle injuries.