First off, are you in a rental or own where you live? If you rent, then that sucks as you'll not invest much and as such will not be able to defeat the noise with much success absent spending some cash...
Dont use Sheetrock, they actually make SOUND BOARD! If you want to do it right, the wall needs air space and the new wall in front cannot be attached to the wall or as little as possible. Otherwise, studs can be attached with a rubber base or pads where screwed or anchored, with a layer of sound board and then sheet rock. Sound deadening insulation can be used in between, but the dead air space would probably perform better. You can expect to lose 3"-4" inches if you want to build a sound deadening wall properly. You could also get some spray foam insulation to fill the existing wall cavity but it's not cheap either...
good luck! Lol...