Given everything you have done and the way in which it is spreading, this is definitely NOT heat rash, and you should have a good argument with your child's doctor! This is entirely too dismissive of you and your child, as well as unhelpful to her recovery.
You also can't keep covering a child with hydrocortizone. I would not get into steroids such as prednisone with a young child, so if you are advised that way, I would ask a lot of questions. I would take it slow with stuff like Benadryl too. Once in a while it's okay, but living on it for a chronic condition is a bad idea.
Besides, these drugs only treat the symptoms, not the cause.
It could be a reaction to detergents, so I would switch to a no-fragrance/no dyes brand, and even use a little less of it unless clothes are extremely dirty.
I would also consider the possibility of some type of food allergy. There is a wonderful children's nutritional supplement (vanilla & chocolate) which helps tremendously with skin conditions such as eczema - I have many friends whose kids have had skin problems caused by various allergies or diet problems, who have had fabulous results. The products work by supporting the immune system and giving outstanding nutrition, sweeping out toxins and allergens. The benefit is, kids often don't get sick much either - no more ear infections, strep throat, etc.!!
The product was formulated by the same scientists who developed Enfamil and ProSoBee, the company has been around 20 years, and the products have earned US government patents, which means there is nothing out there that has the same ingredients or does the same things. The products are not sold in stores because there's no way to give the consumer the same support and guidance. It's sold only through direct marketing, like Mary Kay and other top companies. If you are interested, I would love to introduce you to it! There are some great stories to listen to on conference calls too - some live, some recorded. Depending on where you live, you might be able to come to one of the weekly meetings to learn more. Let me know if you are interested. I'd love to share with other moms!