A classic example of something done almost right . . .
I had a chance recently to perform a "mold' inspection. The occupant of the home complained of mold growth and was particularly concerned about the stripes that were growing on his walls.
I performed a visual exam the walls but the issue was obvious as soon as I entered. .The striping effect I saw is typical marking that occurs in older homes that limited wall insulation and (generally) a four-inch wall cavity.
The striping is not a biological growth but the result of house energy dynamics and occupant behavior. In the wintertime, the studs are substantially cooler than the cavity spaces. The movement of warm air is to the cooler stud, consistent with the Second Law of Thermodynamics. When the air reaches the painted drywall surface, it deposits oils, dust, and smoke on the surface. The reason that the nails show more on the wall surface is that they are metal and better transmitters of energy, and thus colder.
A lot older houses that had smokers exhibit these types of stripes. Other causes are the cooking greases and smoke from the kitchen, oil-based air fresheners, wood fireplaces, and candles.
Candles are a biggie.
So my advice is not to panic. Clean the walls, and then assess which of the likely causes put the particulate matter into the air in the first place. Once you determine that, you have a means of control.