How to choose correct value of inductor in a circuit
It sounds like the inductor is not rated for the current.  You want 2 A average out, so the inductor must be rated for more than that.  Purchasing a component from a local market without a datasheet is no way to source parts.

The LM2567 is a rather old part requiring high inductance.  I've only looked at the first page of the datasheet, but it says right up front that it only runs at 52 kHz fixed frequency.  That requires a large inductor.

You need to actually read the datasheet.  Right on page 1 it shows a Schottky diode.  Your 1N4004 is totally inappropriate here.  It's long reverse recovery time is probably significantly stressing the LM2576.  That may actually be the real cause of the failure.  The inductor appears to be the problem after the LM2567 output fails shorted to the input.

Especially when you don't really understand how something works, you need to follow the directions carefully.