The modern method of having braces installed differs entirely from the traditional way. The actual fitting hardly ever hurts, but the pressure against your teeth and the new sensation will lead to arching and some soreness. You might feel the pain on your lips and gums, but that is because your mouth is not used to the plastic or metal tissues. If everything goes as premeditated; you should have the pain going away after some weeks. If the pain persist, you should go back to your tooth doctor and let them know.