I'm assymetrically tense in my body. Likely because of computer usage, holding a mouse for many hours a day.I like Alexander Technique and Qi-Gong. Yoga can do wonders too. My experience is that you need to stick with whatever thing you pick for a while to see lasting improvement, assuming it works for you. I know people who have tried some various things like 1-5 times and then given up because there wasn't enough improvement. You need to commit a bit longer than that.
It may be that your right hand technique is faulty. I don't think you should be feeling tension with good technique and certainly not to the point of tendinitis.My advice would be to improve the technique in your right hand and learn to move with efficient movements in a relaxed way that doesn't create unnecessary tension.I'm probably not the best to give advice on how to achieve it and certainly not over the internet but a good teacher should be able to help you with that.
Thanks for your reply, I have not heard of qi gong, but I will check it out. So far, yoga seems to work the best. I have also tried feldenkrais, but it just seems like a worse version of yoga and kinda cult-like with it's excessive veneration of its founder (sorry to feldenkrais enthusiasts). And I feel you about the computer usage, I am a SWE myself so that's a big problem for me as well. I even sometimes map my mouse buttons keyboard keys to distribute it a little bit.