Welcome Nick. First, please update your display name to be your first and last name.
Second, do you have the pain when you are out of the kart? I just popped my ribs Labor Day weekend and I am just now able to lay down on that side of my body after six weeks. Your body could just not be used to the action of racing. After being out of a kart for a while, your muscles will get overworked and will be sore for a few days as well, depending on what shape you are in.
Third, for a Ribtect seat, you want to be snug. What is your weight? If you are moving around in the seat, then I would guess the seat may be too big for you and the newer style of Ribtect vest should eliminate that extra space in the seat.