A close friend shut you out in their time of crisis. What to do?

A close friend - at least that's how I regard her - received news that her elderly mother, who lives in a different continent, has a bad type of cancer. My friend goes to great length to keep the news from me for 5 months. All the while I new something was wrong, based on her avoidance & erratic attitude toward me. I asked, all the answers I got back was "everything was fine". One day she blurted out the news & added that's the way she is: she can talk about a lot of joking things but when it comes to this she wants to be alone. I offered my help if she needs it. I do feel hurt that she did tell a couple of people (whom I consider much less closer to her than I am) about her mom's illness. But I refrain from letting her know my feelings, for I think it is thoughtless & self-centered to shift focus to me while she is in so much stress about her mother's condition. However, it prompted me to think that she had never considered me a close friend (as I thought), therefore my emotional support is useless to her, therefore the concealing. My questions are:
1) Do I have reasons to feel the way I do?
2) She said she would give me update on her mother. She has not. Should I ask, or should I leave her alone?
3) How do I offer/show compassion & support without being intrusive, now that I know my support is not something she values or needs at this time.

Note: I'd like to add the reason I posted this question on this forum is that I'm hoping to read opinions from people who share my personality type as well as from people with opposite type. Thx in advance.