I have pain in my arm, radiating from a lump under my elbow for a week now. My entire arm & hand are swollen and worsening. What could cause this?

Sounds worrisome. This sounds like a bacterial infection or other serious problem. I think it'd be best to seek medical attention asap.
Pain &swelling arm. Swelling associated with pain should be examined by a doctor.You may have an infection or some other condition requiring medical treatment so see your doctor or go to er.