The most common injuries during road traffic accidents are fractures. It is hard to diagnose a condition without the x-rays. However, if you are able to walk and move your hand with little difficulty or pain with no restriction of movements, then the chances of fracture are very low. Ligamentous injuries are also common which will not be seen on an x-ray.
Next Steps
X-ray of the Hand AP & Oblique and X-ray of the Knee Joint AP & Lateral to rule out/in fractures