Hi,
This would most likely be an allergy. The reaction that takes place on your skin is due to the release of histamine in response to an allergen. Allergy is caused by an oversensitive immune system, which leads to a misdirected immune response.
Itchy and swollen red bumps or patches all over the body are the characteristic presentation. This is referred to as allergy rash.
Since you both have the rash, it could be due to insect bites or to the dust as you have mentioned in the post. The reactions vary from person to person.
Allergic reactions can worsen when the body is exposed to heat.
Treatment is to avoid the allergen, which you have tried to do with the measures that you have taken.
Anti-histamines like Cetrizine/Loratidine are the drugs used to block the effects of histamine. You can also apply Calamine or Pramoxine lotion in the bumps to alleviate the itching sensation.
ref:http://www.myonlinewellness.com/topic/adam1000812SS
p.s. the red bumps are small and seem to be in hair follicles and not very big, like 4 or 5 millimeters