Why do the veins in my arm ache?

From another cause?: Veins usually don't cause symptoms unless there is inflammation(phlebitis) or blood clots in them(thrombophlebitis). This rarely occurs in the upper extremities except under unusual circumstances. It's likely that your aching is from muscle strain, nerve compression or sprain of a joint. However if the pain persists or the area is tender to touch see a physician for a precise diagnosis.