The other side of the udder is not swollen is it? If she is so young, then, no, she will not have kidded before.
If that was my goat, I would not milk her. For one thing, she will not like it, not having kidded, and you will struggle I would say. Plus, there will not be much milk after all that. Keep an eye on it, and if you think either the udder or teat is pink, shiny or hard, or changes in any way, then get the vet out. It may not be be milk in there anyway, she could have had an infection.
The goats I had who milked without kidding, had an udder on both sides. It may just be because she was having so much concentrates, but now she isn't things should go back to normal, hopefully.
Try not to worry, if Molly looks ok otherwise, is not kicking her udder or looks ill, she is ok. Just watch for any change in the udder size or any hardness there.