i think it might be heat rash hunni, because with you saying tht it almost fades completely when she cool. and irriatates her when she hot and flustered. i dont think there is much tht you can do in situations like these chick apart from just keep her skin clean and dry and if you do use anything use it for sensetive and dry skin.
i have heard of baby acne before but if it gets really bad take her back to the doctors and demand a second opinion. but i think it should go in time. hopefully the weather wont be this hot for much longer and it should settle quite a lot. im keeping my fingers crossed for ya hun xxxxx