Whites Level is a pretty short descent – so maybe check on the lever position (relative to your fingers/wrists/shoulders). When you are out of the saddle (attack position) take a look at your braking finger (you are braking with one finger?) and your wrists – they should be in a pretty much straight line. If you have the levers angled too far up your wrists will get strained as you ride as the forces will be getting taken by your fingers and your wrists, not by your skeleton.
Next thing would be to check that your levers are as close as you can get them to the bar, and still get full power from them. If you have to overstretch your fingers then you strain them on even shortish descents.
Bigger grips can also help (I'm a big fan of Oury lock-ons)
Sorry – much longer reply than I intended. I hope it is of some use!