Can’t speak from experience about shooting iron bullets or shot in a gun barrel.
Here, however, is a picture of shotgun barrel that was damaged by shooting steel shot shotgun loads (not my pic):
Off the top of my head, the issues with iron over lead are: Less density (which means less momentum, less range, and less penetration), About 2.5 to 3 times harder than lead (increased barrel wear/damage), and iron would have a higher chance to ricochet than lead.
Using iron shot would damage your weapon in short order. If the gun is of throw-away quality or it was a last-ditch effort, it might not be an issue. A thick paper or fabric patch/shot wad might reduce/minimize any damage, however.
I honestly think that shooting an un-patched/un-lubricated/un-jacketed iron bullet in a rifled weapon would catastrophically destroy said weapon and land the shooter in whatever equivalent your story has to a hospital. It would be more dangerous to be the shooter than the target. #P