Swelling and pain in the right side groin area. Swelling is forming in the shape of a sausage. This started after an angiogram?

Hematoma. This most likely represents a collection of blood which oozed into the fatty tissue of the groin after the procedure. This will usually resolve and return to normal over a few weeks. If enlarging or associated with significant pain, you should see your doctor and an ultrasound should be performed.
Horse, It sound like a hematoma at the angiogram site. Get an ultrasound study.