Can someone do a biopsy of it? If they can find skin cancers in your country, they can biopsy it. I'm not suggesting that this is skin cancer, only suggesting that if people in your country are diagnosed with skin cancer, biopsies are possible. This will help determine the cause. If you live in a developed country, it is possible to determine the cause of this.
It looks like a dermatitis, but that isn't usually infectious. It could also be fungal.
Is there mold in your home? Is there a cleanser you are using, either a personal one like a soap, or a household one, that you could all be reacting to?