Brushing, cleaning. Gingivitis or swollen gum tissue is most often caused by inadequate oral hygiene during braces. Angling your tooth brush bristles into the tooth and gum tissue union and gently massaging while watching tv or using computer is suggested. Healthy tissue will typically not bleed. Ask your orthodontic specialist if a prescription rinse might be helpful in your situation.
Cleaning. See your dental hygienist for a professional cleaning. Then, use your electric toothbrush (low setting) and carefully floss. You might also benefit from a waterpik. All depends on how committed you are to maximize your oral health. Go for it !