Help please!!! Heat rash or eczema?

It started off 2 days ago as 3-4 pimples on her face i didnt think nothing of it and the next day there were more pimples... i was thinking baby acne and today i woke up and they are like this on both cheeks and spreading under her chin... they still look like pimples with white heads and now have the real redness to them as well as feeling a little bit scaly and dry and of course how much it has spread... i was thinking eczema but then i realised i have been getting the same rash on my arms and legs... we live in australia out in the dessert and now im thinking heat rash because the air con hasnt been working too well and she loves to sleep on my chest... but i stopped that as soon as i seen the first lot of pimples... would it be a coincidence if we BOTH got eczema at the same time (ive only ever had it when i was 2) or is it more likely to be heat rash? ... we cant get into the doctors until next week and i dont know what to do... because if it is eczema i have to keep it moistirized and if its heat rash i have to just use water and mild soaps and keep her extra cool. Please help it looks so itchy and i know shes been "trying" to itch it she rubs her face constantly on anything she lays on. I really need advice please... my poor angel :'( it looks even worse in real life these photos dont do justice