Heat in the udder can indicate mastitis.....but don't panic yet. I have had maiden goats come into milk on their own accord, but not milked them, and never had one that went on to get mastitis. When you felt Mollys udder, had she just been lying down?!!! If so, her udder would be warm from lying on the ground. If the udder is still the same size, and feels the same as when the vet looked, then its unlikely (though not impossible) its mastitis.
How much hard feed (such as goat mix) are you feeding Molly? How much grass is she on? Too much concentrates (goat mix) for a young nanny, can cause them to get milk. All my young, non milking, or male castrated goats get plenty of hay and grass, but they do not get much goat feed, as I feel they do not need it. They do well enough on what they get and are no way skinny.
Its more important to feed fibre, such as hay than give them hard feed. I am just wondering if you are feeding a lot of that? Can you give us an idea how much Molly is having .....?