There was a time when I didn't realize it, but I was holding the "non-mouse" arm/shoulder kind of up (for some reason). As someone else on here said, kind of shrugging - but just the one. I developed a really nasty knot-type of thing that wasn't just numb, but painful. (I've also gotten numb lower arm from mouse use and cell phone use).
Anyway, with that long-term shoulder-pain thing I did two things. First, I put my set of handweights (little ones ) on my computer desk, and started just kind of stretching my arms and shoulders between times when on the computer. What I found really help, though, was to stretch the non-mouse arm and then hold it behind my back for as long as I could, any time I was typing. It kind of feels like it stretches the area that would otherwise knot up or just be generally tensed. I make it a habit to do a couple of other exercise-type things that make the shoulder/back area feel stretched. In fact, basically, as long as I'm sitting at the computer, I'm pretty much always doing something to keep the shoulder muscles loosened up. It's just a habit now, and I'm not even really aware that I'm doing it. (No more knots or numbness since I realized what was going on with that shoulder.)