My old goat twice had milk stones. Both times, it was difficult to get milk out of the teat and, as you described, when I did it came from different angles, and not a lot either. The end of the teat felled blocked so I squeezed extra tightly and the stone popped out. after that, she milked normally until the second one happened. That did come out as well. The opening on that teat wasn't as big as the other side.