The house has a damp problem and the LL knows it. He has no intention of fixing it because whatever it is it'll be something really expensive. Instead he's charging below market rent for it with the expectation the renter will put up with it. When the damp problem becomes too bad for anyone to ignore, LL will probably sell it as it is without doing any repairs.
The issue isn't it's an old house, it's possible to have old houses that aren't damp.
You'd be daft to throw too much money at fixing up somebody else's property. Any anti-mould measures you try won't work beyond a week or so as you've found out, because they're not addressing the root cause of the damp.
Mould spores from prolonged damp are in the air much sooner than you can see them. By the time you have visible mould, it's bad.
I'm not surprised your child is suffering, can they sleep in another room? If the bedroom could be swapped with another room nobody spends too much time in (dining room?) that would be best for health.
You need to either -
fix the cause (unlikely to be feasible/sensible for you)
heat the room sufficiently (and use a dehumidifier permanently too) to keep it dry enough that mould doesn't grow (this could work out expensive)
or leave it unheated and with permanently open window in the hope it becomes cold and dry enough that mould won't grow (which might mean it's too cold for DC to sleep in)
Long term the only answer is likely to be moving house. It's a rotten situation to be in. 💐