Anatomically speaking, veins do not have the right kind of muscles to make possible the movement you describe.
You probably saw some twitching of the muscles of your neck. Google 'fasciculation.' As you will see, there are many causes for this kind of thing: stress and fatigue are among them, and are usually harmless. You could try a heating pad or microwaving a big athletic sock filled with rice and putting it on the area to see if that helps.
I wouldn't fool around with massage of this part of the neck, because that can cause some ill effects if you don't know what you're doing.
Unless you have some weird symptoms like faintness, dizziness, or nausea, what you're experiencing is probably temporary and not important.
But if this starts happening frequently, keep a journal, and faithfully record when it happens and under what circumstances. After a month or so, you might take the record to your doc and ask if it means anything.