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.

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

and at your age, surgery is the only answer to make it more like the other side.  Wearing a headband can work in infants and should always be tried then if there were concerns.  At your age, surgery is needed to reshape the cartilage.

  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 hope I understand your question.  The use of a headband may help prevent your right ear from folding back when you sleep. However, the headband will not help create a permanent change in the position of the ear in relation to your scalp. Otoplasty surgery may be necessary to do this on a permanent basis.  I am not able to see your picture on a large enough scale to provide you with more specific advice,  in regards to your  anatomy or candidacy for otoplasty surgery.

 Best wishes.