I currently have braces on and had the exact same problem. If you're gums are a reddish or dark pink color it is due to the lack of flossing and dental care. If they are like this you should floss more often and the swelling should go down.
However the reason my gums are so large is due to overgrowth of gum tissue, after my braces come off I have to go somewhere in which someone will remove the parts of my gums that overgrew. If you are experiencing this there really isn't anything you can do incept for the gum removal. Hope this helps;).
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