Warped brake rotors are usually only noticeable under deceleration when the brakes are applied. Usually from higher speeds. But badly warped brake rotors can cause shimmy at low speeds as well.
Another common issue for the Cobalt is the front lower control arms bushings. If the car has over 100,000 miles and you haven’t changed the arms out, it is highly likely. The rear bushing starts to deteriorate and the rubber will crack or separate from the metal parts of the bushing. If this is the case, warped rotors and unbalanced tires can exacerbate this problem and actually cause the bushing to fail by vibrating it to death. The control arm may be moving around. It has to be checked with the suspension off the ground and hanging. It is helped if a pry bar is stuck between the control arm and subframe so it can be moved. Can’t always be moved by hand. A lot of people miss this.
It can be a combination of things being out of balance and worn out at the same time. My Cobalt is soon going to need the lower control arms. The bushings are intact but are starting to separate around the edges. Also has a little squeak to it.