It means the second one. "My heart is closed (so that you can't get in)". Sometimes, it can also mean that you won't have mercy on someone, like as if close-minded can mean that you won't be understanding to something, close-hearted can mean that you won't use your feelings and emotion as in not having mercy or forgiveness.
Actually, Indonesians don't think of liver as the centre of emotions, it is still the heart. But it's just, heart is translated to two different organs depending on the context. When you're talking about feelings, you translate heart as "hati", but when you're talking about organs or anatomy, you translate heart as "jantung" and liver as "hati". Hope this helps :)
It might sound weird in English because we don't usually use this sentence for this kind of expression, but in Indonesian, you say your heart is closed for X when you want to express that you don't want him/her anymore. It's like, if your heart has a door, you won't let this particular person enter, which means you don't give a chance for them to love you (basically you're rejecting them). Or, it could also mean that you won't have mercy on a particular person.