Today my tire blew up and I had to brake by bare rim and, as a result, the rim abraded in one place from 3mm to 2mm.
Can I continue to use this rim or I need to repair it in the shop or order a new rim/entire wheel?
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The rim is toast.
Even if the sidewall is structurally sound (no cracks or anything) that’s too little remaining material to safely retain a tyre (i.e. to properly seat the tyre bead). The tyre probably also won’t sit completely round.
I don’t think this can be repaired, at least not easily or cheaply. You’ll need a new rim.