I'd have it looked at if I were you. Just immobilizing it or whatever is not necessarily going to do... anything whatsoever. I have a similar problem, but something like that has no effect whatsoever.
It's not just the wrist motion that can get you; it's the non-stop clicking (something that designers of these games NEVER think of, sigh...).
Really, get it checked out, because you might regret it later if you dont. In my case, I went through a period of about a YEAR where I could not use the mouse for gaming. It just hurt too much. Like WAY too much. I'd have days where I couldnt use it at all. To play something like Minecraft then, I had to set up the controller to EMULATE the mouse; I've been using that for so long now that it's the only way I play many games, even though I can use the mouse better at this point.
Needless to say, none of that is fun. It really is best to get it checked out sooner rather than later, and instead of just going offa recommendations you get from people. Tendon and/or nerve issues are nothing to sneeze at.