The ones in the third photo look really sore and possibly infected.
It is best to take her to the vet for a proper diagnosis asap, it could be a staph infection.
Also I'm not sure if it's just the photo, but is her anus ok? It doesn't look right to me, or is that just her tail/the angle making it also look not so good? ><
I wouldn't put any oil on her, if it is an infection this will irritate the skin further (since it does not allow the skin to breathe) and can cause or make an infection worse. Not sure about the neosporin, if it was me, I would only bath her in room temp water and take her to the vet asap. Don't use any soaps or shampoos, until her skin has returned to normal.
If she has gotten the spots since coming home, what kind of bedding are you using and if fleece how are you washing it / what kind of detergent ~ regular or scent free? Perhaps it is causing an allergic reaction?