I was interested to learn that "I am full" means "I am drunk," because I have distinct memories of being in high school French and having the teacher warn us never to say, "Je suis plein(e)," which literally means "I am full" but in French means "I am pregnant." :)
And we say that quite a lot in Denmark (especially in December because of "julefrokoster")!
So when a person is "full" in English the implication is "full of food", but in danish the implication is "full of alcohol"?
'I am full' would mean 'jeg er mæt', but if 'the bottle is full of water' then 'flasken er fuld af vand'.