First, isolate the area. Keep kids and pets out of the room. Wear an N95 mask, gloves, and safety glasses. Before cleaning, mix a solution of one part white vinegar to four parts water; avoid bleach as it only removes the colour and can push spores deeper into porous surfaces like drywall. Scrub the area thoroughly with the solution, then dry it completely with a fan. However, this only addresses the surface growth. The underlying cause is almost certainly moisture trapped within the wall cavity itself, likely from condensation due to the temperature difference between the cold AC wall and the humid room air.

Given that the mold is behind furniture and you have ongoing health symptoms, a DIY approach is a temporary fix. The hidden moisture problem will cause it to return. For a permanent solution, a professional assessment is needed to identify and rectify the moisture source, which could require improving insulation, addressing AC condensation lines, or using industrial dehumidifiers. They can also perform lab testing to confirm the mold type, which is prudent with children experiencing respiratory issues. For a problem of this nature, the fastest way to truly resolve it safely is to get a diagnostic inspection.