The adhesive left on the teeth is removed with a special bur (an attachment for the dental drill) that is designed not to remove any enamel. However, the drill spins the bur at high speed, and when it touches the surface of the tooth you may feel some sensitivity (the bur heats up and the heat irritates the tooth). Once the adhesive has been removed, the teeth are polished until they are smooth. The final, perfectly smooth feel comes after a few weeks, thanks to the polishing action of your toothpaste and toothbrush.
This answer is for general information. Your own case needs an examination by an orthodontist.