With no offense really, to anyone, WOW, I see answers, that don't address the more important issues.
First of all the "wet" is coming from somewhere. It isn't akin to the "immaculate conception." You state that the exterior wall is dry, have you checked the roof? especially above what I assume is a window (Single glazing?)
On that note be aware that WATER finds its way, and very often the source is nowhere near the place it manifests in its travel.
I recently replaced drywall in a basement level of an 11,000 sq. ft. building, because of water, its damage, and Black Mold as the byproduct. BLEACH will not strictly "Kill" it, nor will it stop whatever is causing it. Might there be "plumbing" running through that wall, to a bathroom/lavatory?
Sadly your best efforts won't rid your "mind" of the situation, and as you dicover the source/reason for the "wet" you might consider checking your budget for new carpet, as well as repainting, at the least.
You also don't strictly state the humidity in your location, or within the home, in general. Opening a window might not actually "HELP." A dehumidifyer appliance would certainly show you in a span of time, how much moisture is in the air.
Black mold is "Life" on some level, and GROWS as it is nourished. In this case by something you should address along with removal of all that "Houses" the mold.
One more note: Without knowing the substance of the wall, IE: Drywall/sheetrock (Gypsum filled, paper covered panels) I offer this. In such case as drywall is the case, the mold is attacking the paper and paint on the surface of the wall, as well as the back side of the panel. It does not attack the plaster/gypsum, that makes up the substance of the wall. To retrace to the bleach suggestion. Certainly with bleach and scrubbing you can remove or diminish signs of mold on the interior of the wall, but if it is "Drywall" the mold is established on the back side and your efforts will be time wasted. "Removal" might be the only option.
First and foremost however is to explore and discover the source, then deal with its after effects.
Steven Wolf
(The Rev.)
Source(s):
40 plus years as a contractor