Polish it mirror bright. Both barrels.
Then clean and oil post shoot as normal.
You have differential corrosion due to different microfinishing between the barrels.
One side provides greater tooth to the oxygen in the atmosphere than the other side, so it rusts faster. Or at least as your eyes see the rust flowering it does.
I keep oil wipes in the door of my truck. No gun gets cased without a wipe down. Chambers as well. They dispense like baby wipes. Read that idea someplace else. It has been a good one.
