Your problem is due to braces. There is lot of calculus deposition that makes the gums to swell and get inflamed. Please use an orthodontic brush and a plaque
removing mouthwash always till you have the braces on. For immediate relief, please use a gum astringent
eg. Dentakind astringent. This will reduce the puffiness and bleeding of the gums. Please get scaling done for better results. Take care!