What muscle in my arm is hurting?

Picture a brick on a table. You are sitting at the table, and the brick is in front of you, pointed away from you (i.e. the long way is pointed “forward” and “back” rather than side to side). You stick out your right arm and put the elbow on the table, positioned so you can wrap your thumb and fingers on either side of the brick and lift it up. You lift it up with the elbow remaining on the table, your arm extended forward while lifting.

When I do this I have a sharp pain in the muscle that bulges upwards nearish and to the right of the inside of my elbow (a couple of inches wrist-ward of the inside of my elbow). What muscle is this?

Brachioradialis?

Possibly tendonitis and not the muscle. Try a tendonitis strap (elbow brace, tennis elbow strap, compression strap) around your forearm and see if the pain goes away. The strap stops your tendon from sliding along bone in your elbow as you lift something. You don’t need a strap to try this out, you can just grasp your forearm from the top with your other hand just forward of your elbow, or use a belt or something to try it out.

Wow, I think that might be it. When I squeeze my right forearm with my left hand while lifting something, the pain definitely lessens and may go away entirely.