Wet wall in baby's room

[Nerel]

I noticed bad damp in the cupboard of our baby's bedroom recently. The wall was black behind various objects piled up in there.
We cleaned all of the cupboard with bleach and painted it with a bathroom anti mould paint.

I've since then noticed the wall in there actually has streaks of water running down it. It's a dark cupboard with no ventilation, built into the outside wall. It's hard to see but I can't tell where the water is coming from or properly see the outside wall but as far as I can tell there's no damage. There is some sort of tape and plaster missing at the top of the cupboard but it has been like that since we moved in a few years' ago and as far as I know nothing has come off / broken.

Does anyone have an idea of what might cause this and how best to figure it out / fix it, please?
I am thinking of getting a dehumidifier anyway as all of our windows suffer from bad condensation and our baby (just turned 1) has just been given an inhaler as he's constantly wheezy. We might move him out of that room for now.

I would have thought moving your baby from the room would be imperative and a matter of urgency to prevent exacerbating health issues.

Masking a damp wall with paint and using a humidifier won't stop the problem. You need to locate the source and get it fixed by a professional.

Regarding condensation, do you ventilate your home by opening windows? Sounds as if you need to if you aren't already. Are you drying clothes in radiators. This too can cause damp/mould/condensation.

condensation on an exterior wall, inside or behind furniture, is common.

The causes are excessive water vapour in the air, commonly caused by insufficient ventilation plus sources such as hanging wet washing over radiators, or steamy bathrooms with no effective extractor fan. It can be caused just by breathing and perspiration, but this would only happen if ventilation was extraordinarily bad.

You can space the furniture away from the wall, and ventilate the room by opening the window every morning, but you also need to address the source of water vapour.

Water vapour is lighter than air so will rise through the home until it either escapes, or finds a cold surface to condense on.

Rarely the source is a leak, such as a radiator pipe, gutter, or bath.