I am an orthopedic physical therapist. I see elbow injuries quite frequently, but I need a little more info. Is the pain on the inside or outside bone when your palm is down? Does it hurt at all to make a strong fist? Does it hurt to bend your wrist (with your palm facing down) backward against resistance.
I would guess by your brief description that you have tennis elbow, also known as lateral epicondylitis. This occurs when you frequently do activities that require you to pull your wrist backwards. The muscles that do this go from the back of your fingers to a bump on the outside portion of your elbow called the lateral epicondyle. When these get over used, they tighten up and pull on the insertion point. If this is done in escess, the outside covering of the bone called the periostium becomes inflammed. The 2 points that usually hurt with this, are the common extensor tendon (where the muscles that pull the wrist back all start from), and the lateral epicondyle.
If this is actually what it is, you can do a few things. 1st, ice it. It is an inflammation injury, so anything that helps decrease the injury will help. Antiinflammatories may also help such as ibuprofen or naproxen (aleve). I would advise approval from your physician to make sure they don't interact with any other health issues or meds you are on. The problem is really an overly worked, overly taught muscle. This muscle needs to be stretched out to decrease its pull on the bone, and then strengthened to allow it to tolerate normal function again.
http://www.nismat.org/ptcor/tennis_elbow/
This site has an excellent description of the injury, and a good basic rehab protocol with pictures of good stretches and ex's. It also shows the brace that I would recommend. It is a counter-force brace that pushes the tendon down so it can not pull on the bone so hard.
Pool is not something that should cause this. That means that you either do something repetitively during the day that aggravates it, or your pool bridge is being done with too much active extension (pulling wrist backwards). Since the pain began when you started playing more, it is probably your bridge. I would consider adjusting it, or the problem will likely continue to resurface. Try relaxing your hand on the table as muc has you can while shooting. PM me or ask away with anymore questions or info.