Tennis elbow or golfers elbow doesn't have to be from playing tennis or golf. They are terms used for tendonitis of the elbow. Athletes or office workers can all suffer from them. To prevent the onset of these conditions, contrary to some common sense, you need to work out your shoulder, neck and elbow together to eliminate the root causes of these conditions, not just stretch and strengthen your elbow and wrist.
There are two reasons why this is the case. First, all nerves controlling muscles in the arms are from the neck. You will need to maintain a good posture and neck flexibility to ensure no pinching to the nerves, so that the muscles will function at the optimal level. Secondly, your shoulder is the base for you to move your arm. Without a strong and stable shoulder, you will have to put extra stress on your forearm and elbow to be able to perform at the same level. After a while, pain and injuries will start as a result. So when you experience any elbow pain and discomfort, you should also check your posture and shoulder strength and flexibility in addition to stretching your elbows.
In a clinical setting, most cases we see, there are most likely to be some issues with the neck and shoulders. While you get treatment for your elbow pain, if the other problems are not solved, the results would be sub-optimal.