Self-ligating brackets usually have a rounded rectangular shape, because their front surface has a small built-in door that holds the archwire in the centre of the bracket. Conventional brackets, by contrast, hold the archwire in place with small elastic ties that have to be attached to the brackets. For this reason, conventional brackets have a more retentive shape, designed for hooking the ties on, and this particular shape can cause discomfort and injure the sensitive lining of the mouth. Studies show that self-ligating braces cause less discomfort and reduce the risk of mouth sores.
This answer is for general information. Your own case needs an examination by an orthodontist.