if your gums bleed when you brush, it means there is bacterial infection in that area...so by not brushing , you let the bacteria stay and grow even more!!!
dosn't matter how much it bleeds, continue brushing, but never be harsh on your gum, try to use a soft or even extra soft bristle brush ( some dental offices do have extra soft toothbrushes that they order directly from dental supply companies)....what type of floss you use/??? of course with the brackets and wires you can't use a regular floss , you need Floss threader in order to reach in between....
again *** dont' worry about bleeding, when you see bleeding, continue brushing , and dont' get discourage****
dont' use listerine mouth wash...since your gums are very irritated , since listerine has alcohole in it, USE ACT mouthwash because it has fluoride which is good for you specially now that you're having braces!
try to hold the brush at 45 degree angle to your gum lines ( when tooth meets the gum) and kinda giggle the brush gently and massage your gum, you can also use rubber tip ...your gum needs stimulation right now ....
don't worry , you will be fine .
i'm very sorry and disturbed to see that stupid orthodontist that treats you didnt' give you good instruction about maintaining oral health!! it really makes me mad when i see such people working !!! they MUST give you written instruction or atleast reffer you to hygiene cleaning!!!!!!!!!!!!!!!
i'm a hygienist and previously i worked as an RDA for an orthodontist