[Quiet Man Cometh]

You're not supposed to scratch at bites because of health and bacteria and the like, breaks the skins, etc. There are topical remedies you can get, and some anecdotes. Personally, I would put a band-aid over it to stop your bra from rubbing at it. I do that myself also to keep me from scratching. If you still rub the bandage, as least you aren't getting your nails on the bite.