Yes, I had extreme elbow pain in only my left elbow every time I rode more than 10 miles or so. It would get worse with distance. Never hurt any other time but riding my one bike. It was in fact the only real acute PAIN I had while biking. Tried all kinds of different fixes- stems, bars, saddle positions. And I never rode with my elbows straight locked or tense. I tried to ride relaxed. The pain was the same as yours- if I didn't keep shaking my arm out and bending my elbow every couple of minutes, the pain would be so bad that I felt I couldn't bend it. Oddly, no major trouble with the other elbow.
The problem i DID have with that bike is that it was designed for a man and had a top tube that was too long for me, plus my weight was centered too far over the crank and onto my hands. No matter what we tweaked and no matter how much my core muscles improved over the thousands of miles and 2 years, I always felt like my weight was falling forward too much and always had the awful one-elbow pain.
Finally I ordered a custom bike made to my body measurements. My weight is balanced nicely further back, and I don't feel like I'm falling forward anymore. I can even ride no-handed now that I'm not having to hold myself up with my hands.
When I first rode my new bike, the elbow pain seemed less. Now, after 500 miles on my custom bike, the elbow pain has slowly faded away and is now gone. What a huge relief!
Hope this proves helpful in some way.