Based on your complaints and picture seems like you need to give some rest to your hands. This seems like work related tendonitis. Means inflammation of your muscles and tendons of your hand. Could be a ganglion cyst too. Needs examination by a Surgeon or Orthopaedician.
Next Steps
Consult a General Surgeon or an Orthopaedician
Health Tips
Rest to your hands. It happens when you keep your wrists unknowingly in a different position. A splint might help