That's a pinch grip with the index finger and the middle finger drawing the bow. The index finger does two jobs: pinches the arrow along with the thumb and also helps to hold the string back. If the ring finger was also helping to draw back the string, it would be called a tertiary grip. Many NA tribes used this grip (shown in the picture).
The soreness should be in your finger tips (index finger and middle finger) and not in the joints.