I second the "allergic" reaction to something.
I've seen several different versions of allergic rash/reactions.
It could be somethign complicated like "food" issues, or it could simply be the laundry detergent on her bed, or your own clothes (i assume you snuggle and hug your new pup..lol).
usually (although not always) if its under the skin (red dots , that dissapear when you push on them) its usually an "internal" agent (something ingested, or gone INTO the body in some way).
If the bumps are raised, and or on the OUTER layer or skin (and the redness does not dissapear when you press on them) its an outside agent (something she's come in contact with or laid on, or has sprayed onto her...ect.
This is not always true...there are a few acceptions. But that is the general rule of thumb I've been told.
From what I'm seeing on the photos, you have more of a "contact" issue than an "ingested" issue.
Try to contact her old owner and find out if she's ever had this before.
And then ask her what all she "used' on her.
Start listing ALL the changes you've made. (shampoo, flea meds, any kind of spray, laundry detergent, even a humans perfume can set her skin off if she's snuggled and such alot).
Ruby once had an attrocious looking rash on her belly, and I was racking my brain on HOW , WHAT ..ect. Then I realised...I'd used a "different" solution to clean the carpet than I usually do. I carpet cleaned it all out with several doses of hot water...and gave her benedryl. She cleared right up. She also will sneeze her head off, if I use a paticular carpet powder or spray fabreeze. I have to put her outside to spray the fabreeze and keep her OUT of the room that has the carpet powder (resolve moist powder stuff).
If you ask her previous owner about all her "things" she used. And then compare it to the list of yours. It will give you a good starting point. And if nothing else..you can give the list to your vet..and they can tick off the "highly unlikelys" and at least give you a good shove in the right direction.
GOOD LUCK. I know its frustrating to be so HAPPY they are there, and WHAM...health issues.