I do not have plasterboard on my wall, but I do have various internal walls of plasterboard.
They cause no problems at all.
However, I believe the plasterboard manufactured and sold in Denmark is slightly different to that sold in Britain.
Here we size plasterboard with a thin solution of wallpaper paste, allow this to dry then paper and paint the walls, finally affixing skirting boards on full-lenght walls, or beadings if needed, where an upper wall meets , say, a kitchen counter.
Are you sure that the walls you suspect of causing your cough are actually plasterboard? I ask because various forms of interior walling material from the 1970s and '80s contain formaldehyde, which can cause the problems you name.