White stuff coming out of my wall when dry
That would be efflorescence on a concrete wall. Efflorescence is when water passes through the wall and evaporates on the surface. The minerals contained within the water can't evaporate, so they stick around, usually looking like a fine white powder on the surface. You can see the same thing with hard water that evaporates from a kitchen sink. It's not harmful to the wall, but it is ugly and will eventually ruin the paint, because the paint is likely impermeable to moisture (if it is acrylic, latex, alkyd, or oil-based), so it will bubble and peel over time as the water in the wall tries to escape.

The root cause is moisture movement through the wall, or, simply put, the wall getting wet. To prevent this, keep the wall from getting wet. Typically this is the job of the roof, but the wall itself can have its own protections. If the wall is simply a monolithic concrete slab with no finishing on the outside, that would contribute to the problem too. Broadly, what you want to do is to keep water out of the wall's core while letting water already there escape to the exterior side.

The cheapest solution would be to paint the exterior side of the wall with a breathable, vapor-permeable paint (e.g. a silicate mineral paint--NOT a typical paint!). The more complete and permanent solution would be to cover the exterior side of the wall with some type of breathable, vapor-permeable weather barrier substance (e.g. liquid-applied water-resistive barrier material, housewrap, asphalt-soaked paper) and then put up bricks or some other decorative covering.