One Ear Protrude from Folding when Sleeping?

A headband really won't make any difference in the appearance of your ear.  The cartilage needs to be reshaped with an otoplasty procedure.  The procedure is done through an incision behind the ear and provides a permanent and very reliable correction.

  A head band may temporarily help hold the ear in place, but the permanent solution is an otoplasty. The procedure is performed under local anesthesia and involves making a fold in the ear cartilage and setting at back closer to the scalp.

I agree with you that based on the photo, your left ear does look more prominent. A head band will temporarily help the left ear to sit closed to your head but this will be very short lived. The only permanent solution to "pin back" the left ear is an otoplasty procedure. This would re-create the natural fold in the left ear and place the rim of the ear closed to your head. I hope this information is helpful.Stephen Weber MD, FACSWeber Facial Plastic Surgery