Why polish will not fix peeling clear coat
Polish works on the surface; it cannot make a separating clear layer stick again or replace coating that has come off. When clear coat loses its bond with the color beneath it, the affected area may need sanding and refinishing.
Peeling or just dull paint?
Dull paint does not always mean the clear coat is peeling. The surface may look worn while the clear layer is still in place. A shop needs to check the finish itself before recommending polishing or refinishing. Photos can show the area you are concerned about, but they cannot confirm whether the coating is lifting or how far the failure extends.
Does one peeling panel need a full repaint?
A problem on one panel does not automatically mean the whole car needs paint. The shop can assess where the coating is failing and discuss whether refinishing an affected panel or a larger area makes sense.