The best rule to follow when performing resistance training, or any training, is to stop when it hurts. Pain is your body's way of protecting itself, and the pain that you are feeling in your elbow is a sign that something is not quite right. While I know that you might feel pained at having to skip your upper body workout for a day or two, taking a few days off now can help prevent chronic pain and mobility issues in the future. Utilizing the proper technique and appropriate warm up can also help to make sure that you are able to enjoy these activities long into the future.
Cartilage, the buffer at the ends of many of our long bones as in the elbow, does not have blood vessels. Because of that, the only nutrition and waste product removal that our cartilage gets is by the stretching and squishing actions that occur with relation to the cartilage. Because of that, appropriate stretching before exercising "plumps up" your cartilage so that it can appropriately buffer the contact of your bones on each other. Additionally, stretching helps to optimize the strength and tension of ligaments and tendons to avoid strain injuries. Please speak to your doctor
if your pain continues, and avoid lifting weights until it resolves.