Rash down both sides, armpits, back of arms in a 5yo female

[MishiaMama]

I have a little girl who just turned five. She has had two upper respiratory infections and an ear infection in the last month and still has a persistent cough. Last Wednesday (20th), she began to complain that she was itchy. Friday a rash showed up on her torso, under her armpits, only on her sides down her ribcage.

Nothing has gotten the rash to go away. We have washed everything repeatedly, soaked her in epsom salt, oatmeal, and baking soda baths (not all at the same time). Her pediatrician gave her two rounds of antibiotics. We even gave her Benadryl. She has had no change in environment, no new food, no new detergents or lotions, no new clothes, etc. Nothing has changed and none of the remedies have helped.

The rash now stretches from inside her armpits down to her hips, covering about four inches on both sides of her torso. It is also down the inside and back of her upper arm, halfway to her elbow.
It looks almost like heat rash, very tiny red bumps and redness on the skin. It blanches when pressure is put on it. She says it is very itchy and it seems to be getting worse.

Her pediatrician is at a loss. He recommended we go to a dermatologist but with the holidays we can’t be seen until mid-December. She’s miserable and I don’t want to wait that long.

Any suggestions?

Thank you!