If the index finger is broken, it will be too painful to even move it. A sprained finger can be moved and the swelling will not be too much. Try and use some ice cubes and take pain relievers and if this does not help, it will be important to take it to the doctor for it might have broken.
If you cannot move it without sever pain, it's probably broken. If it is broken, it should heal in 4-6 months without a doctor. I broke my middle finger once and didn't go to the doctor and it was fine, but you might want to see one just in case.