Just go with the rythm. I like to compare osu! to malabarism, since when you do malabarism, you don't focus on every ball you throw up into the air - you look up, toss the balls, they enter your field of vision, begin to fall and you position your hand depending on how you calculate its landing spot. Because I don't have to focus on every hitcircle to land a hit, if I just stare on the center of the screen I can have a good preception of the whole area and move my hand accordingly (that may be because I play with a 15" laptop monitor though.) Anyway, the less you move, the less stress you'll create. sometimes my wrist starts to hurt in the middle of a song, and that ruins my concentration so I concentrate the weight of my arm in my elbow, lift my wrist and hover my hand on top of the zx keys, and that makes it easier for me to do streams without getting tired...
Anyway, I sometimes suffer with that and found out doing the following helps me a lot - cover up your combo while you're playing. I used to non intentionally look at my present combo and that would make me nervous all of a sudden - if I had a high combo, I'd start missing beats and ruin the playthrough. I don't play the same map 50 times without interruptions either, I play it three times at best then try it again another day. Sometimes you paly a map so many times you're no longer in the ideal mindset for playing osu, so it helps.