The gums can react in different ways while a patient is wearing braces. When the gum is irritated by bacteria, it reacts by swelling, turning red and bleeding easily. In this situation, many patients start avoiding brushing that part of the mouth so as not to make it bleed. This is actually the opposite of what you should do. The gum swells when too many bacteria build up around or under it, or when food gets trapped there. Its defence reaction is to increase its blood supply, because the blood contains many cells that fight inflammation. To calm the gum down, we need to deal with the cause of the inflammation – namely, the bacteria. Thorough brushing, careful flossing with a scraping, sawing motion and an anti-inflammatory mouthwash will calm the gum and make it shrink back within just a few days. Clean the problem area perfectly and don't be afraid that it will bleed – the important thing is to remove the bacteria, plaque, tartar and any other similar irritants.
This answer is for general information. Your own case needs an examination by an orthodontist.