Tight 'Cord' from Armpit

I have a strange cord(tendon, vein or something) that is extremely tight only on the right side when I place my right hand behind my head or raise the arm overhead(pullup/overhead press). It begins in the armpit and is about 3-4 inches toward my elbow.

It is visible only while the arm is raised upward. Anyone have an idea as to what this might be?