I would check with a doctor. I have swelling in my left hand because of some damage from a car accident. Nothing in the hand was broken, but I think I severely jammed several fingers. It has been 7 months and there is still a little swelling there. I think swelling in the fingers can take a long time to go away, especially if it is in your non-dominant hand. My therapist told me to make a fist and spread out my fingers alternately as much as I could, and it did seem to help at first. I think the idea is to get blood flow going and help your body naturally take care of it's swelling. Now that I'm down to just a little swelling, progress is very slow.
If nothing hurts, doing the fist and spread fingers thing won't hurt you.