^^^ Yup, that's edema, very common :) My one mare, Ruby, gets it pretty early in her pregnancies, and it's on the entire belly!
I think her udders will fill up more. As she gets closer/fuller, it'll be easier to milk them. But here's my experience:
I could never really get milk out. Usually when I did, it was only a drop or two, and within the week of foaling. My last foal was a dummy foal, he couldn't figure out how to nurse. So I tried milking my mare to try to bottle feed him, but could barely get anything out. When my vet got here, she milked her, no problems. I told her I had problems getting milk, so she showed me how, and wallah! I got milk! I don't think I could explain how... I've read explanations, but that never worked, I had to be shown. Sorry!