In general, our ears are not completely symmetrical. Most often, these asymmetries are noted more by the patient than by their family and friends. I would advise you to leave your ear alone. If you must have surgery, a small incision can be placed inside the helical rim and a small amount of cartilage shaved. The scar should heal nicely and the rim will be less notched. That said, even having surgery, don't expect your ears to be completely symmetric.
I do agree with you that there is a marked difference in the shape and contour of your two ears. However, to put you at ease nobody ever has this type of side by side comparison of a person's ears in normal social settings. Further, we really don't spend any time looking at a person's ears. Unless an ear is very prominent, we typically do not pay attention to them and spend our time looking at the eye area.
With that said, you do appear to have a variant of a Darwinian tubercle which could be shaved down through a well hidden incision as suggested by Dr. Kontis. I hope this information is helpful for you.
Stephen Weber MD, FACS
Denver Facial Plastic Surgeon
All patients have minor asymmetries from their right and left sides of the face. While reviewing your pictures, I appreciate the differences in the shape of your right and left ear. Depending on the severity of this difference, a minor procedure to remove a small area of the cartilage could improve the symmetry, but asymmetries would remain. Depending on your goals, the results you are seeking may not be possible. In that case, I would not suggest that you undergo a procedure.
I hope this helps.