Rest is important for recovery however there are a few caveats. Resting too much can stiffen joints and prolong rehabilitation, the idea of weeks of bed rest are long gone. Gentle range of motion exercises can speed healing and reduce inflammation. Range of motion exercises can even begin on the same day of injury. Rest in the terms of RICE is really limit pain producing activities, don't do anything to make the injury worse.
Ice sprained joints and strained muscles during the first 48 hours post injury. Leave the ice on for 10 minutes at a time with at least one hour between sessions and limit it to 3-4 times per day. Icing beyond the initial 48 hours can actually slow healing as it limits blood flow.
Compression is one of the most under utilized strategies. Gentle joint compression with a tensor bandage or sleeve can help limit inflammation and can even help move it out of the effected joints. Be careful to not compress to the point of pain.
Elevation is also helpful for extremity injuries. The closer the injury is to your heart the less effective. Elevation helps drain inflammation and effective for wrist and ankle injuries.
Make sure you have your injury assessed for stability and function by a professional. It is important to know what you are dealing with and whether there may need further imaging assessment.
Dr. Nelson