If when you run a fingernail over it, if your nail catches in the scratch, the scratch is very likely too deep to fix with paint correction(like buffing/polishing).

A proper fix will require prep, painting and blending, which you shouldn't try to do yourself. You could buy a touch up stick that matches your paint to cover the scratch. It won't look perfect and won't last forever without clear coat on top, but it will prevent rust.

Before you decide how you'll deal with this, you can bring it to a body shop for an estimate, most shops will do that for free. Most shops can give you an estimate from photos emailed or submitted to their websites.