Does this mean close to "My heart is closed (to others, it only has room for you)" or "My heart is closed (so that you cannot get in)"
If it's the latter, it should be "My heart is closed TO you"
I was thinking the same thing.
Secondly, how does hati mean two different organs?
I might be wrong, but I think it's a case of the liver being considered the centre of emotions in Indonesia, not the heart.
Not sure if you can apply a literal translation here. Although it may make sense in Indonesian, the translation of "Hati say tertutup bagi kamu" could simply mean "I do not need/want you any more".