Pain when bending elbows

I really want to build up my arm strength and tone that flabby part under your arms, but whenever I target that muscle, there's a tendon or something that I can feel dragging back and forth over the tip of my elbow joint and after like 2 reps it really hurts. I have hypermobile elbows, which may or may not be related to that happening. What exercises can I do to avoid that pain? Maybe more importantly, what exercises can I do to strengthen my elbow and maybe stop that bad feeling from happening? Is there a particular video on this website I could follow that addresses this goal?

Edited