Wrist / Hand Injury

So I caught an edge (wheel got caught in a vertical groove) on my bike a few weeks ago , and went over the handlebars.

It's been about four and a half weeks since the accident, and all my road rash is nicely healed but I've still got some pain in my right wrist. I've found that I still can't do weights or swimming without some pain, and even putting weight on it while cycling is a bit unfomfortable. I want to train, but I'm afraid of making it worse if I push things.

Now here's the tricky part. I don't have health insurance (long story) so I haven't seen a doc or had an X-Ray done. So I never got an actual diagnosis. When it happened I had some swelling, but not very much and it cleared up within a day, so I don't think I broke anything. The pain is in the lower portion of my hand, around the area of the ring/pinky finger tendons and (if I swim with my ring and pinky fingers "open" that seemed to relieve a lot of the pain but kills my effectiveness). Turning my hands palms up and putting pressure on my ring/pinky fingers causes pain, as does putting pressure on the ball of my hand (like a push up). I've been wearing a brace to keep it (relatively) immoble (even when sleeping) and that seems to have helped me some. But I guess my question is... is there anything more I can be doing to speed the healing process? I guess I'm just frustrated that it's taking me so long to get full use of it back. Also does this sound like it's just a bad sprain, or should I be more concerned?