Does the Right Hand Know what it's Doing?

The fingers of my right hand stiffen with tension when I play the flute, and this is, to say the least, deleterious to my playing. When I first began playing the flute, my left hand bothered me because of the unaccustomed hand position. I was getting cramps in my left hand, but after a few months they went away. Now it's my right hand, partly because you use your right pinkie to steady the flute, and partly because the fingering is slightly different from that of the saxophone, which I'm used to, and I have to concentrate. And there are deeper psychological reasons, which, possibly makes the problem of  interest to people who don't play the flute.
I discovered something that is interesting even to people who don't try to play fast sixteenth notes on a wind instrument by making an effort to relax my right hand all the time, both to improve my flute playing and because I'm also feeling some pain in my hand and forearm when I use the computer and manipulate the mouse, and pain is something one tries to get rid of.
Making an effort to relax is rather paradoxical, and my main method has been, first of all, to notice the tension in my hand rather than ignore it. Just noticing that I'm pressing the keys on the flute as well as on the computer keyboard too hard is a start toward not pressing them too hard. I have found that dealing with that tension in my hand has also improved my tone on the flute, and my playing sounds more musical (the clicking of my keyboard remains as unmusical as ever, but I type better when I relax my fingers).
I believe that tension in one's dominant hand has to do with the desire of the dominant hemisphere of brain to keep everything under control. Write something with a pen or pencil, or draw a picture, and check on whether you are pressing the writing instrument harder on the paper than you need to in order to leave a mark. Try to write or draw using as little pressure as possible. I bet your writing, both the handwriting itself and the content of your writing, as well as your drawing, will be freer and more imaginative if you lighten up the pressure of the pen.
I believe the pressure in my right hand when I play the flute is connected with anxiety. I'm still not sure that the flute will, in the words of my teacher, Raanan Eylon, cooperate with me, so I try too hard to force it to cooperate. I blow too hard and grip the instrument too hard, and the flute resists rather than cooperating. If one is confident, one doesn't have to make too much of an effort to do what one wants to do, and one's confidence is rewarded by success.