Might be a problem with an addon, try turning them all off and see if that fixes the problem; then try:
If it DOES fix it:
Turn off half your addons, if the problem is not there: it's in the other half
And just keep turning on and off half your addons until your find the problem,
so if you had, 100 addons, try 50, 25, 12 6 3 1. ;D BAM. Then just go to the config for that addon and change the config of that character on an alts (or reset it) and/or delete the wtf file for that addon.
If it DOESN'T fix it:
Try repairing your game via C:\Program Files\World of Warcraft\Repair.exe
If the problem still persists, try calling their support line:
Link.
But to me it sounds like an addon function JUST on that character that is messing up your screen.