To prevent rust you must keep oxygen and moisture (including water vapor) from the previously rusted surface, which would be very difficult in your circumstance. From what I can see you have also not removed all the rust. There are some products that will chemically convert the rust to a stable surface, but may turn the pitting black or grey. You then have to decide whether to leave it that way or paint with chrome paint. If you paint you need to further sand the surface, and if you don't paint the existing surface may further degrade.