I very much doubt you are a cold-hearted person. It is far more likely that you did a lot of your grieving when he got the diagnosis and you have been expecting this for a while so you are just relieved/happy to have had more time with him than you expected.

There are a wide range of "normal" responses to a death and the fact that yours is different from your mum's, your sister's and your aunt's doesn't mean it's better or worse. Just different.

It is also possible that it will hit you after he dies, even some time afterwards and you will be more upset then. Or you might not.

Another possibility is that you find it hard to grieve. Given what you said about it being embarrassing that you cried in a situation where it is very normal to cry, it's possible you are somebody who puts a lot of effort into being strong and taking care of everybody else and at some subconscious level, you don't feel like you can cry or get visibly upset.

But your feelings aren't an indication of how kind or good-hearted a person you are. Getting upset isn't something to be embarrassed about and not getting upset isn't something to feel guilty about. Neither is something you fully control and neither is right or wrong. You feel what you feel and how upset you are isn't an indication of how much you loved the person.

If I had to guess, I'd say it is that you were expecting this and that he lived longer than expected, so you have accepted it, but there are a whole load of possibilities and none is morally wrong.