lizzy - In my experience, anything that goes into a goose or ducks mouth comes out its nose at some point. I don't worry about water seeping, or being blown, out of their nose unless there is some other indication of a problem. I have even marveled how they can spatter water all over long after they have taken a drink. Where do they store it?
The goose shaking her head - I think that is what you said and I am not going back through all these posts,

You might make sure her nostrils or whatever they are called, are clear and don't have anything stuck up there. I found one of my geese with a piece of dried grass suck up there. You can also feel along her neck to again, make sure there is nothing stuck. Remember it takes a bit for anything they have eaten to go down that long neck. I have a slighty daffy goose that will eat the finer type feed so fast she stuffs her neck tight. One night she did that, acted like she couldnt breath and it took me several minutes of squeezing that mass to get it brocken up enough she could blow some out and finish swallowing some. She is the only one that does that though.
If they are eating and generally acting ok, they are probably ok. Not eating and isolating themselves from the others are the things to watch for. And any problems with walking or balance. A goose sitting by itself when the others are moving around is to be checked out.