+1 to the comments about hand on top near stem, and looking down the road.
Don't look at the bottle cage; look where you want the bike to go, and it will keep going there.
Also, bend your elbow and relax. Keeping your arm tense is likely part of your problem.
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You could fall off a cliff and die.
You could get lost and die.
You could hit a tree and die.
OR YOU COULD STAY HOME AND FALL OFF THE COUCH AND DIE.