Welcome to you and your baby
SO glad you got her out of that terrible situation.
Sorry to say, but your Mollie should probably see a vet. If she is scratching to the point of giving herself sores, there could be something that needs medication. My two are highly allergic to fleas and will develop a secondary skin infection if it's left too long without vet care. They get an anti-inflammatory shot to stop the itch cycle.
What kind of food are you feeding her? This may have something to do with her dry skin, as well.