When I bought the car my tires were low on.

Tires have nothing to do with the feel of the brake pedal. You could have no tires, even no wheels, and the brake pedal would feel normal.

The problem you described only occurs on GM vehicles and is due to uninformed do-it-yourselfers. There is likely some other problem causing the low pedal, but regardless, it is never advisable to push the pedal more than half way to the floor on any brand of car more than about a year old. Doing so can damage the master cylinder from running the lip seals over the crud and corrosion that build up in the lower halves of the bores where they don't normally travel. In addition to that, on GM cars there's a valve that will trip in the master cylinder and block fluid flow to two ports, one front wheel and the opposite rear wheel. If the master cylinder has not already been damaged, the only way I've ever found to reset that valve is to go to the caliper that's not working or flowing any fluid, open the bleeder screw, then give it a very short, quick burst of compressed air, then let it gravity bleed.

Bleeding isn't what I said to do. If a caliper isn't working it's because the port in the master cylinder is blocked by a valve. You have to give a short burst of compressed air into the bleeder screw to force brake fluid to go back up to the master cylinder to open that valve. Until you do that, the left caliper isn't going to work.