On the left side of my neck my vein really pops out when I'm laying down. Also my left arm and chest seem to be a little swollen. Is this a cause for?

Venous distension. My concern with arm and ad chest swelling is superior vena cava syndrome which may be from an obstructing mass. Jugular venous distension May also be fro Congestive heart failure - see a doctor ASAP to rule these out.
Need more info. It would be helpful to know if you are over weight or very slim. Your age is also important. It could all be anatomically normal but nevertheless it should be investigated by your family physician.