To make runs "sound right", you need to respect the phrasing. Just because something is played fast doesn't mean that you can't play with dynamics (obviously). So when you're working with the runs, really look at them, and see if adding a swell, or "leaning into" a beat will make it sound more coherent. If you have no idea where to start, pick a beat to lean into at random, and see if you like it better! Singing the melody is my favorite way to pick out which parts of a phrase need a little more "oomph".
Like other people said, when your hand gets fatigued, take a break. There's no point in playing through it, because that just makes it easier to get hurt. Over time, your musculature will develop and you'll be able to play for longer without getting that fatigue. Anything you can do to stay relaxed will delay that fatigue. I find that playing with "proper piano technique" (according to my teachers, wrists high, fingers curled) is really really annoying at first, but over time, it did wonders for my stamina.
As far as shoulder tension is concerned, make sure that you're sitting at the right height and the right distance from the piano for you; try playing out of a different chair, or adding a cushion on top of your bench. Also, consciously make sure that you're not tensing up your shoulders, it'll help you with your control over time (tired muscles are imprecise muscles).