Could be mud fever or a fungal infection. Whilst these types of things often start on the surface, any small cut or abrasion can allow it to penetrate the surface of the skin. With mud fever, the skin will often crack thus providing a point of entry for bacteria and other nasties. If left untreated some infections can enter the bloodstream and become systemic, something you will need a vet to check out.
I think you may have 2 issues going on and both of them stem from the mud. I think she may have a skin infection and may also be dealing with bruising. I agree with sarahver. I also would ask the vet about dosing her with some Dexamethasone (Azium) for the swelling in her legs and skin irritation…she may or may not have an infection, but she certainly seems to be having a negative reaction to something in her environment. Perhaps it is the combination of both mud and the type of shavings in her stall. Mud and water will cause the hoof to soften, the photos show her standing on very rocky soil, soft hooves and hard rocks = bruising. Personally, I'd call the vet and tell him your concerns about her having a skin infection and then I'd have the farrier out to check for bruising and thrush.