Is sacroiliac joint dysfunction chronic, or will I recover completely?

Depends. Si joint dysfunction can be chronic or acute, depending on the cause and length of time one has had symptoms. In general, si joint dysfunction is due to inflammation of the si joint; prolonged inflammation can result in arthritic changes to the joint surface. Inflammation can be reversed (thus tends to be acute) but arthritic changes can not be reversed. See your doctor if in prolonged pain.
May be. If chronic you can control the pain by taking sij injection.