3 weeks after my facelift, one ear is throbbing and painful.

Occasionally patients have pain around the ear which can persist a few weeks. I would check back with your surgeon. It could be another stitch or piece of one, an irritated nerve or some other cause of inflammation. Point tenderness can also respond to a steroid shot. The good news is that in my experience pain like this is always temporary.

The fact that one side is more painful than the other after a facelift is not totally unexpected. This pain should be getting better as the days pass.

While the right and left sides of the face may heal at different rates following a facelift procedure, throbbing pain in one ear three weeks after surgery is not typical. Seeing your surgeon, preferably within a day or so, is important to evaluate and treat the problem. An infection could be the issue. Other causes of the pain, such as nerve pressure or entrapment, are also possible and can be evaluated at the same time. Best regards.

I recommend you return to your surgeon for an examination. There could be an infection or a retained piece of suture causing irritation. 

Thank you for your question.  An examination would be needed , please return to your surgeon so they can examine you.  All The Best