smell rotten eggs when under hard acceleration

When passing another car and you accelerate hard "to the floor with the gas peddle" we get the smell of rotten eggs. It goes away after about two or three minutes of normal driving. I would love to donate to you cause but at this time we are broke do to me having double lung transplant and have even maxed out our credit cards. I am on the wan down with a short time to live and really need to leave my wife a good safe car.