If I'm understanding your description of where the pain is correctly, the only thing you can do aside from going to a doctor or getting an elbow brace, is to stretch it out. Whenever I'm doing a bench press or a dumb-bell curl, I get this sharp pain in my elbow thats not on the bone or skin, but its definately underneath the skin. What I do to fix it is keep using my elbow until the pain goes away. I know it sounds like a perfect way to make it worse, but thats just what I do.
