I'm sorry for your lose Lotty.
It seems strange that you "weren't sure" whether to tell your "good friend" about your father dying... Why weren't you sure? What held you back from telling her? Did you think she might react strangely?
I lost my dad very unexpectedly, nearly 3 years ago, and it was incredibly difficult. But I was also surprised by some reactions. Most people were as you'd expect, very sympathetic and "can I help at all?", a number went above and beyond in a way I didn't expect. For example, the wife of a cousin, who had also lost a parent very suddenly, reached out regularly and deeply with love and support. We are not close, but I've not forgotten her kindness.
In contrast, a cousin I practically grew up with had nothing to say at any point, whereas her sister was wonderful.
People do strange things in the face of unexpected tragedy. If you want or need more from your friend, absolutely ask for it. This is one of the very few times in life when you can say "it's all about me right now".
I read something a while ago about circles of family/friends/acquaintances relating to a personal tragedy. In essence, you should show love inwards, towards those closer, or as close to the tragedy as yourself (your mum, siblings, grandparents, your children), and then vent outwards, towards friends and acquaintances.