Get some emollient susch as Cetroban or Epimax for you hands . I get Cetroban on my reapear but, Epimax does the same thing and is alot cheaper, and considerably cheaper than going gluten free.
You could also place a bowl of water near a radiator or buy radiator hangers such as these that help the humidityy in the room and the dry heat rad’s give off.
At the more expensive end, you could fit a PIV unit