is a relatively common condition. This is also known as lateral epicondylitis. I would recommend that you discuss this with your primary care doctor
-- this should be evaluated.
Tennis elbow (or shooter's elbow) is a type of repetitive stress injury. This means that the problem arises from doing a movement multiple times -- it does not necessarily need to be tennis -- but needs to be an activity that moves the hand in a similar motion. This causes inflammation of the outside (thumb side) of the elbow. The inflammation actually occurs where the tendons/muscles insert on the bone. Therefore, to answer your question, typing could cause tennis elbow depending on how you type and the orientation of your keyboard. If the inside (and not the outside) of your elbow is causing the pain -- then you could have medial epicondylitis or Golfer's elbow.
There are many other causes of elbow pain. Olecranon bursitis is also relatively common type of elbow pain.
Typing rarely causes tennis elbow -- because the elbow is not often used in typing. That being said -- it is possible. The more common typing related repetitive stress injury is carpal tunnel syndrome
which causes hand and wrist pain.
This should be evaluated by your doctor. Tennis elbow can be treated. Good luck!