Besides a skin problem which is what it looks like on the surface ...being that you just got her it could also be flea bites or mites.....just mentioning does not mean that it is one of those but if it is you do not want them to populate on her. Some dogs do not scratch, so it is hard to tell if they have these little monsters until it shows nasty signs.
I hope she is ok but it is important to get her to a Vet...I would say ASAP.
good luck let us know how she is
tina
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