the reason you can be told you're too full to eat something, even though your hunger display shows that you're hungry, is that you can fill up on poor-quality food, or even on too much liquid. these have bulk, but not so much nutrition.
suggestions for dealing with this:
eat better food, such as waybread or breadfruit. these are nutritious and they don't fill you up much.
drink from the sanctuary island fountain, or from a container filled from there. it'll quench your thirst yet isn't so filling.