If I have a lymph node or cyst on top of coroided artery right side. Could it cut off the blood flow and cause a blood clot?

Carotid body tumor. You might have a mass near neck artery called the carotid. If this is what your doctor told you, then carotid body tumor/mass is the topic. The mass usually forms just behind the artery, right where it separates into its two branches. You should get referred to a vascular specialist. And yes, there are potential complications, as you list. However, the potential is low with vascular specialist.
Neck swelling. Matt, since the supposed cyst or lymphnode is outside the artery, unless it is huge, there won't be mechanical compression and blood supply cut off. Blood clot, it is not simple to answer without feeling this swelling and considering work up depending on what your physician thinks. A simple cyst doesn't cause blood clot. Let your physician examine you.