Sounds to me like you have inflammation, tendinitis or whatever in your Brachioradialis. Very common place to get it. Symptoms you mention are very similar to what most guys complain about. The pain radiates like a mother too, and is probably why you feel it in the elbow area. Reason it is so common is just about everything you do requires the Brachioradialis to be incorporated. And most lifters do not target the area training wise specifically.
There are a lot of short term solutions to the pain. Elbow sleeves, icy hot, stop pain etc. If you have good insurance go see a sports specialist they will know much more about your possible injury than just a regular Doctor. Just go to make sure there is no serious issue. Time off, and a slow return with massage therapy while slowly strengthening the area is the best bet. Pick up a pair of wrist straps. Use them during back and shoulder workouts ( raises etc for shoulders ) to take some of the strain off of your Brachioradialis.
http://en.wikipedia.org/wiki/Brachioradialis