First, only arteries have the muscular structure that allows them to pulsate. Veins, even the largish jugulars, do not pulsate, because they cannot.
So, what you're probably seeing is the pulsation of one of your carotid arteries, which actually lies fairly deep in the neck. On thin people, the pulsing is more visible because there's less fat between the skin and deeper structures.
This pulsation is perfectly normal. In some people, the pulsing can be seen on *both* sides. You have just become aware of it, and now it's got your attention.
You can google something like 'visible neck pulse' for more info. But it would be healthful to put the flashlight away for anything other than getting around in the dark.