helloo..read thru ur query..accordingly i feel that there is nothing much to be worried in this..swelling in the gum (gingivitis)is common during brace treatment.Bleeding from gums due to gingivitis is common..nothing to be worried just be careful with ur oral hygiene thats it..but do see that whether there is any laceration or abrasions of gum or cheek due to braces which can also cause bleeding usually...In my opinion there is nothing to be worried(i am not seeing the clinical condition) but if u want u can go to a dentist get scaling done...and besides thatfollow good oral hygiene practices like brushing (u get orthodontic brushes) do mouth washing(listerine is good for gum problems).do salt water gargling also twice daily(removes any infection if present)above all be happy and cool...happy and cool mind is a great medicine for all diseases...hope ur benefitted something from this reply...have a healthy day!!!!