I'm not sure exactly where you're describing the pain, but it sounds like tennis elbow (lateral epicondylitis)?
Definitely track down and eliminate what's causing it. I don't have anything to add to what Lisa and Mudmucker said or what you've already tried. I assume that by saying your elbows are relaxed, you mean they're not locked and you're absorbing any vibration in your triceps, pecs and spinal muscles.
But in the meantime, try stretching the forearm by holding the arm straight out from the shoulder, extending the wrist and pulling back on the fingers, then flexing the wrist and doing the same. Massage down the whole length of the flexor muscles on the top of the forearm is good, too. And epsom salt soaks (although it was a challenge for me to find a tub big enough to accommodate my forearm, hand and elbow but small enough to fit on the arm of a chair).
Speed comes from what you put behind you. - Judi Ketteler