did she just have the kids??
one of my boer goats did the same thing, the colostrum was so thick it would barely come out, we milked out the really really thick stuff and after a while it started flowing normally. one of my goat raising neighbors said it was normal, and nothing to worry about, but i think i will have it checked out further next time it happens

Do you have any way to restrain her? I was thinking you need to dip the whole bag, or at least that whole side in a bucket of warm water to loosen it up. Before you do that---it that side swollen and warm? She could have mastitis. If you don't think she has mastitis, try getting the kid to nurse from that side to get things flowing. You notice how they "bang" the bag as they suck, try that if you try the warm water trick.
Good luck.