Have sharp pain outside the left side of throat near artery is this a lymph node? feels swollen, trouble swallowing, had wisdom tooth infection

Lymph node chain: There's a chain of lymph nodes right in that area you describe. If u had a recent infection on that side, then it's likely u have a swollen lymph node. What I don't like is the trouble swallowing -that means you should go back to the surgeon who extracted your tooth for a look. It's their responsibility since they did your surgery. You don't want infections of the head/neck getting out of control.