Yeah...you're better off with a new liner. When a liner floats it lifts off the bottom...typically. You can feel the water under it as it is squishy. The liner popping out of the bead is probably just due to the fact the water level is real low and stressed it. A liner will float if the ground water level is higher than the level in the pool. If it isn't floating now with the low water level, it probably didn't float to cause the damage. You don't say where you live so I don't have any idea what your ground water situation is like.
As for the liner companies I can't help you there...sorry.
Al