Sweep Electric White

A couple of days ago, i visit my dentist and he said my gum was infected. So, he used a electric tool to clean my gum. Unfortunately, my gums were bleeding a lot! Apparently, i have notice a tiny piece of my gum is missing and it is now showing a tiny bit of the teeth. Will my gum grow back?? (plzz say yes) Everytime I brush my gumline (the part that is showing some white teeth) is bleeding a lot. Should i keep brushing or should i just quickly sweep over it. And not spend a lot of time on it because im a afriad that, that particular area of gum might go away. Aside, from that particular arrea is painful. the front teeth gumline also hurts. By the way, i have braces.

My real question is : Should i brush the (injuries) gum for a very long time? even though it bleeds (a lot) and part of my gum is missing.

Also, in my mouth the very last tooth located on the bottom right beside it, there is a large part of gum and on the side is painful. Why?