Removing braces with pliers involves putting some pressure on the teeth. The most sensitive teeth are the upper and lower front teeth, and they may feel pain during the procedure. This sensation passes in an instant and doesn't need an anaesthetic (the discomfort of having the anaesthetic would be greater). Metal braces are the easiest and most comfortable for the patient to have removed, because the metal bends under the pressure of the pliers and comes away from the tooth. Ceramic and sapphire braces don't bend and may break during removal. Don't worry if you hear a crunching sound – the bracket is made with a weak point that is designed to break when needed without damaging the enamel.
This answer is for general information. Your own case needs an examination by an orthodontist.