My right elbow joint is sore on the inside, and as soon as l start using my mouse, my hand goes numb. Why is this happening?

Nerve compression. Pain in the elbow associated with hand numbness. Specifically the pinky and ring fingers can be caused by cubical tunnel syndrome or pressure of the ulnar nerve at the elbow. Other causes of hand numbness include carpal tunnel syndrome which is pressure on the median nerve in the hand. Suggest seeing a hand surgeon and getting an emg.
See below. Symptoms and concerns like these mandate a thorough evaluation by your doctor. Only after such an evaluation, which may include labs and radiographic examinations, can he/she let you know what's going on and how best to help you.