For the last 3 days I've had extreme pain in my left elbow and lower arm. What could that be?

Elbow pain. The most common cause is tennis elbow, or lateral epicondylitis. This is the result of a partial tear of the muscle from the bone. Initial treatment is ice, a medication like motrin, and a wrist splint to keep the pressure off the elbow at night. If that is not successful, see an orthopedic surgeon, who can do a cortisone injection, or even operate to fix it.
Many Possibilities. Extreme pain should always be evaluated by a visit with a physician. Pain is an indicator something is wrong. Pain in this area can be related to bursitis or arthritis affecting the joint and radiating downward this would be associated with redness, swelling and tenderness. The other possibility that comes to mind is nerve impingement in the neck, shoulder or elbow. Seek help soon.